Daily Papers

Estimating physical properties for visual data is a crucial task in computer vision, graphics, and robotics, underpinning applications such as augmented reality, physical simulation, and robotic grasping. However, this area remains under-explored due to the inherent ambiguities in physical property estimation. To address these challenges, we introduce GaussianProperty, a training-free framework that assigns physical properties of materials to 3D Gaussians. Specifically, we integrate the segmentation capability of SAM with the recognition capability of GPT-4V(ision) to formulate a global-local physical property reasoning module for 2D images. Then we project the physical properties from multi-view 2D images to 3D Gaussians using a voting strategy. We demonstrate that 3D Gaussians with physical property annotations enable applications in physics-based dynamic simulation and robotic grasping. For physics-based dynamic simulation, we leverage the Material Point Method (MPM) for realistic dynamic simulation. For robot grasping, we develop a grasping force prediction strategy that estimates a safe force range required for object grasping based on the estimated physical properties. Extensive experiments on material segmentation, physics-based dynamic simulation, and robotic grasping validate the effectiveness of our proposed method, highlighting its crucial role in understanding physical properties from visual data. Online demo, code, more cases and annotated datasets are available on https://Gaussian-Property.github.io{this https URL}.

Realistic simulation of dynamic scenes requires accurately capturing diverse material properties and modeling complex object interactions grounded in physical principles. However, existing methods are constrained to basic material types with limited predictable parameters, making them insufficient to represent the complexity of real-world materials. We introduce a novel approach that leverages multi-modal foundation models and video diffusion to achieve enhanced 4D dynamic scene simulation. Our method utilizes multi-modal models to identify material types and initialize material parameters through image queries, while simultaneously inferring 3D Gaussian splats for detailed scene representation. We further refine these material parameters using video diffusion with a differentiable Material Point Method (MPM) and optical flow guidance rather than render loss or Score Distillation Sampling (SDS) loss. This integrated framework enables accurate prediction and realistic simulation of dynamic interactions in real-world scenarios, advancing both accuracy and flexibility in physics-based simulations.

We introduce PhysGaia, a novel physics-aware benchmark for Dynamic Novel View Synthesis (DyNVS) that encompasses both structured objects and unstructured physical phenomena. While existing datasets primarily focus on photorealistic appearance, PhysGaia is specifically designed to support physics-consistent dynamic reconstruction. Our benchmark features complex scenarios with rich multi-body interactions, where objects realistically collide and exchange forces. Furthermore, it incorporates a diverse range of materials, including liquid, gas, textile, and rheological substance, moving beyond the rigid-body assumptions prevalent in prior work. To ensure physical fidelity, all scenes in PhysGaia are generated using material-specific physics solvers that strictly adhere to fundamental physical laws. We provide comprehensive ground-truth information, including 3D particle trajectories and physical parameters (e.g., viscosity), enabling the quantitative evaluation of physical modeling. To facilitate research adoption, we also provide integration pipelines for recent 4D Gaussian Splatting models along with our dataset and their results. By addressing the critical shortage of physics-aware benchmarks, PhysGaia can significantly advance research in dynamic view synthesis, physics-based scene understanding, and the integration of deep learning with physical simulation, ultimately enabling more faithful reconstruction and interpretation of complex dynamic scenes.

The integration of Supernumerary Limbs (SLs) on humanoid robots poses a significant stability challenge due to the dynamic perturbations they introduce. This thesis addresses this issue by designing a novel hierarchical control architecture to improve humanoid locomotion stability with SLs. The core of this framework is a decoupled strategy that combines learning-based locomotion with model-based balancing. The low-level component consists of a walking gait for a Unitree H1 humanoid through imitation learning and curriculum learning. The high-level component actively utilizes the SLs for dynamic balancing. The effectiveness of the system is evaluated in a physics-based simulation under three conditions: baseline gait for an unladen humanoid (baseline walking), walking with a static SL payload (static payload), and walking with the active dynamic balancing controller (dynamic balancing). Our evaluation shows that the dynamic balancing controller improves stability. Compared to the static payload condition, the balancing strategy yields a gait pattern closer to the baseline and decreases the Dynamic Time Warping (DTW) distance of the CoM trajectory by 47\%. The balancing controller also improves the re-stabilization within gait cycles and achieves a more coordinated anti-phase pattern of Ground Reaction Forces (GRF). The results demonstrate that a decoupled, hierarchical design can effectively mitigate the internal dynamic disturbances arising from the mass and movement of the SLs, enabling stable locomotion for humanoids equipped with functional limbs. Code and videos are available here: https://github.com/heyzbw/HuSLs.

While there has been significant progress in the field of 3D avatar creation from visual observations, modeling physically plausible dynamics of humans with loose garments remains a challenging problem. Although a few existing works address this problem by leveraging physical simulation, they suffer from limited accuracy or robustness to novel animation inputs. In this work, we present MPMAvatar, a framework for creating 3D human avatars from multi-view videos that supports highly realistic, robust animation, as well as photorealistic rendering from free viewpoints. For accurate and robust dynamics modeling, our key idea is to use a Material Point Method-based simulator, which we carefully tailor to model garments with complex deformations and contact with the underlying body by incorporating an anisotropic constitutive model and a novel collision handling algorithm. We combine this dynamics modeling scheme with our canonical avatar that can be rendered using 3D Gaussian Splatting with quasi-shadowing, enabling high-fidelity rendering for physically realistic animations. In our experiments, we demonstrate that MPMAvatar significantly outperforms the existing state-of-the-art physics-based avatar in terms of (1) dynamics modeling accuracy, (2) rendering accuracy, and (3) robustness and efficiency. Additionally, we present a novel application in which our avatar generalizes to unseen interactions in a zero-shot manner-which was not achievable with previous learning-based methods due to their limited simulation generalizability. Our project page is at: https://KAISTChangmin.github.io/MPMAvatar/

Self-supervised pretraining from static structures of drug-like compounds and proteins enable powerful learned feature representations. Learned features demonstrate state of the art performance on a range of predictive tasks including molecular properties, structure generation, and protein-ligand interactions. The majority of approaches are limited by their use of static structures and it remains an open question, how best to use atomistic molecular dynamics (MD) simulations to develop more generalized models to improve prediction accuracy for novel molecular structures. We present SURrogate mmGBSA (SurGBSA) as a new modeling approach for MD-based representation learning, which learns a surrogate function of the Molecular Mechanics Generalized Born Surface Area (MMGBSA). We show for the first time the benefits of physics-informed pre-training to train a surrogate MMGBSA model on a collection of over 1.4 million 3D trajectories collected from MD simulations of the CASF-2016 benchmark. SurGBSA demonstrates a dramatic 27,927x speedup versus a traditional physics-based single-point MMGBSA calculation while nearly matching single-point MMGBSA accuracy on the challenging pose ranking problem for identification of the correct top pose (-0.4% difference). Our work advances the development of molecular foundation models by showing model improvements when training on MD simulations. Models, code and training data are made publicly available.

Dynamic 3D interaction has been attracting a lot of attention recently. However, creating such 4D content remains challenging. One solution is to animate 3D scenes with physics-based simulation, which requires manually assigning precise physical properties to the object or the simulated results would become unnatural. Another solution is to learn the deformation of 3D objects with the distillation of video generative models, which, however, tends to produce 3D videos with small and discontinuous motions due to the inappropriate extraction and application of physics priors. In this work, to combine the strengths and complementing shortcomings of the above two solutions, we propose to learn the physical properties of a material field with video diffusion priors, and then utilize a physics-based Material-Point-Method (MPM) simulator to generate 4D content with realistic motions. In particular, we propose motion distillation sampling to emphasize video motion information during distillation. In addition, to facilitate the optimization, we further propose a KAN-based material field with frame boosting. Experimental results demonstrate that our method enjoys more realistic motions than state-of-the-arts do.

In this work, we present a novel physics-based data-driven framework for reduced-order modeling of laser ignition in a model rocket combustor based on parameterized neural ordinary differential equations (PNODE). Deep neural networks are embedded as functions of high-dimensional parameters of laser ignition to predict various terms in a 0D flow model including the heat source function, pre-exponential factors, and activation energy. Using the governing equations of a 0D flow model, our PNODE needs only a limited number of training samples and predicts trajectories of various quantities such as temperature, pressure, and mass fractions of species while satisfying physical constraints. We validate our physics-based PNODE on solution snapshots of high-fidelity Computational Fluid Dynamics (CFD) simulations of laser-induced ignition in a prototype rocket combustor. We compare the performance of our physics-based PNODE with that of kernel ridge regression and fully connected neural networks. Our results show that our physics-based PNODE provides solutions with lower mean absolute errors of average temperature over time, thus improving the prediction of successful laser ignition with high-dimensional parameters.

We introduce a novel masked pre-training technique for graph neural networks (GNNs) applied to computational fluid dynamics (CFD) problems. By randomly masking up to 40\% of input mesh nodes during pre-training, we force the model to learn robust representations of complex fluid dynamics. We pair this masking strategy with an asymmetric encoder-decoder architecture and gated multi-layer perceptrons to further enhance performance. The proposed method achieves state-of-the-art results on seven CFD datasets, including a new challenging dataset of 3D intracranial aneurysm simulations with over 250,000 nodes per mesh. Moreover, it significantly improves model performance and training efficiency across such diverse range of fluid simulation tasks. We demonstrate improvements of up to 60\% in long-term prediction accuracy compared to previous best models, while maintaining similar computational costs. Notably, our approach enables effective pre-training on multiple datasets simultaneously, significantly reducing the time and data required to achieve high performance on new tasks. Through extensive ablation studies, we provide insights into the optimal masking ratio, architectural choices, and training strategies.

Human motion capture from monocular videos has made significant progress in recent years. However, modern approaches often produce temporal artifacts, e.g. in form of jittery motion and struggle to achieve smooth and physically plausible motions. Explicitly integrating physics, in form of internal forces and exterior torques, helps alleviating these artifacts. Current state-of-the-art approaches make use of an automatic PD controller to predict torques and reaction forces in order to re-simulate the input kinematics, i.e. the joint angles of a predefined skeleton. However, due to imperfect physical models, these methods often require simplifying assumptions and extensive preprocessing of the input kinematics to achieve good performance. To this end, we propose a novel method to selectively incorporate the physics models with the kinematics observations in an online setting, inspired by a neural Kalman-filtering approach. We develop a control loop as a meta-PD controller to predict internal joint torques and external reaction forces, followed by a physics-based motion simulation. A recurrent neural network is introduced to realize a Kalman filter that attentively balances the kinematics input and simulated motion, resulting in an optimal-state dynamics prediction. We show that this filtering step is crucial to provide an online supervision that helps balancing the shortcoming of the respective input motions, thus being important for not only capturing accurate global motion trajectories but also producing physically plausible human poses. The proposed approach excels in the physics-based human pose estimation task and demonstrates the physical plausibility of the predictive dynamics, compared to state of the art. The code is available on https://github.com/cuongle1206/OSDCap

Interlocking brick assemblies provide a standardized yet challenging testbed for contact-rich and long-horizon robotic manipulation, but existing rigid-body simulators do not faithfully capture snap-fit mechanics. We present BrickSim, the first real-time physics-based simulator for interlocking brick assemblies. BrickSim introduces a compact force-based mechanics model for snap-fit connections and solves the resulting internal force distribution using a structured convex quadratic program. Combined with a hybrid architecture that delegates rigid-body dynamics to the underlying physics engine while handling snap-fit mechanics separately, BrickSim enables real-time, high-fidelity simulation of assembly, disassembly, and structural collapse. On 150 real-world assemblies, BrickSim achieves 100% accuracy in static stability prediction with an average solve time of 5 ms. In dynamic drop tests, it also faithfully reproduces real-world structural collapse, precisely mirroring both the occurrence of breakage and the specific breakage locations. Built on Isaac Sim, BrickSim further supports seamless integration with a wide variety of robots and existing pipelines. We demonstrate robotic construction of brick assemblies using BrickSim, highlighting its potential as a foundation for research in dexterous, long-horizon robotic manipulation. BrickSim is open-source, and the code is available at https://github.com/intelligent-control-lab/BrickSim.

Deep generative models such as flow matching and diffusion models have shown great potential in learning complex distributions and dynamical systems, but often act as black-boxes, neglecting underlying physics. In contrast, physics-based simulation models described by ODEs/PDEs remain interpretable, but may have missing or unknown terms, unable to fully describe real-world observations. We bridge this gap with a novel grey-box method that integrates incomplete physics models directly into generative models. Our approach learns dynamics from observational trajectories alone, without ground-truth physics parameters, in a simulation-free manner that avoids scalability and stability issues of Neural ODEs. The core of our method lies in modelling a structured variational distribution within the flow matching framework, by using two latent encodings: one to model the missing stochasticity and multi-modal velocity, and a second to encode physics parameters as a latent variable with a physics-informed prior. Furthermore, we present an adaptation of the framework to handle second-order dynamics. Our experiments on representative ODE/PDE problems show that our method performs on par with or superior to fully data-driven approaches and previous grey-box baselines, while preserving the interpretability of the physics model. Our code is available at https://github.com/DMML-Geneva/VGB-DM.

The Sun's outer atmosphere, the corona, is maintained at mega-Kelvin temperatures and fills the heliosphere with a supersonic outflowing wind. The dissipation of magnetic waves and direct electric currents are likely to be the most significant processes for heating the corona, but a lively debate exists on their relative roles. Here, we suggest that the two are often intrinsically linked, since magnetic waves may trigger current dissipation, and impulsive reconnection can launch magnetic waves. We present a study of the first of these processes by using a 2D physics-based numerical simulation using the Adaptive Mesh Refined (AMR) Versatile Advection Code (VAC). Magnetic waves such as fast magnetoacoustic waves are often observed to propagate in the large-scale corona and interact with local magnetic structures. The present numerical simulations show how the propagation of magnetic disturbances towards a null point or separator can lead to the accumulation of the electric currents. Lorentz forces can laterally push and vertically stretch the magnetic fields, forming a current sheet with a strong magnetic-field gradient. The magnetic field lines then break and reconnect, and so contribute towards coronal heating. Numerical results are presented that support these ideas and support the concept of a symbiosis between waves and reconnection in heating the solar corona.

Developing embodied AI agents requires scalable training environments that balance content diversity with physics accuracy. World simulators provide such environments but face distinct limitations: video-based methods generate diverse content but lack real-time physics feedback for interactive learning, while physics-based engines provide accurate dynamics but face scalability limitations from costly manual asset creation. We present Seed3D 1.0, a foundation model that generates simulation-ready 3D assets from single images, addressing the scalability challenge while maintaining physics rigor. Unlike existing 3D generation models, our system produces assets with accurate geometry, well-aligned textures, and realistic physically-based materials. These assets can be directly integrated into physics engines with minimal configuration, enabling deployment in robotic manipulation and simulation training. Beyond individual objects, the system scales to complete scene generation through assembling objects into coherent environments. By enabling scalable simulation-ready content creation, Seed3D 1.0 provides a foundation for advancing physics-based world simulators. Seed3D 1.0 is now available on https://console.volcengine.com/ark/region:ark+cn-beijing/experience/vision?modelId=doubao-seed3d-1-0-250928&tab=Gen3D

Reconstructing biomechanically realistic 3D human motion - recovering both kinematics (motion) and kinetics (forces) - is a critical challenge. While marker-based systems are lab-bound and slow, popular monocular methods use oversimplified, anatomically inaccurate models (e.g., SMPL) and ignore physics, fundamentally limiting their biomechanical fidelity. In this work, we introduce MonoMSK, a hybrid framework that bridges data-driven learning and physics-based simulation for biomechanically realistic 3D human motion estimation from monocular video. MonoMSK jointly recovers both kinematics (motions) and kinetics (forces and torques) through an anatomically accurate musculoskeletal model. By integrating transformer-based inverse dynamics with differentiable forward kinematics and dynamics layers governed by ODE-based simulation, MonoMSK establishes a physics-regulated inverse-forward loop that enforces biomechanical causality and physical plausibility. A novel forward-inverse consistency loss further aligns motion reconstruction with the underlying kinetic reasoning. Experiments on BML-MoVi, BEDLAM, and OpenCap show that MonoMSK significantly outperforms state-of-the-art methods in kinematic accuracy, while for the first time enabling precise monocular kinetics estimation.

Tactile feedback is critical for understanding the dynamics of both rigid and deformable objects in many manipulation tasks, such as non-prehensile manipulation and dense packing. We introduce an approach that combines visual and tactile sensing for robotic manipulation by learning a neural, tactile-informed dynamics model. Our proposed framework, RoboPack, employs a recurrent graph neural network to estimate object states, including particles and object-level latent physics information, from historical visuo-tactile observations and to perform future state predictions. Our tactile-informed dynamics model, learned from real-world data, can solve downstream robotics tasks with model-predictive control. We demonstrate our approach on a real robot equipped with a compliant Soft-Bubble tactile sensor on non-prehensile manipulation and dense packing tasks, where the robot must infer the physics properties of objects from direct and indirect interactions. Trained on only an average of 30 minutes of real-world interaction data per task, our model can perform online adaptation and make touch-informed predictions. Through extensive evaluations in both long-horizon dynamics prediction and real-world manipulation, our method demonstrates superior effectiveness compared to previous learning-based and physics-based simulation systems.

We present PhysGen, a novel image-to-video generation method that converts a single image and an input condition (e.g., force and torque applied to an object in the image) to produce a realistic, physically plausible, and temporally consistent video. Our key insight is to integrate model-based physical simulation with a data-driven video generation process, enabling plausible image-space dynamics. At the heart of our system are three core components: (i) an image understanding module that effectively captures the geometry, materials, and physical parameters of the image; (ii) an image-space dynamics simulation model that utilizes rigid-body physics and inferred parameters to simulate realistic behaviors; and (iii) an image-based rendering and refinement module that leverages generative video diffusion to produce realistic video footage featuring the simulated motion. The resulting videos are realistic in both physics and appearance and are even precisely controllable, showcasing superior results over existing data-driven image-to-video generation works through quantitative comparison and comprehensive user study. PhysGen's resulting videos can be used for various downstream applications, such as turning an image into a realistic animation or allowing users to interact with the image and create various dynamics. Project page: https://stevenlsw.github.io/physgen/

Physics simulation is paramount for modeling and utilizing 3D scenes in various real-world applications. However, integrating with state-of-the-art 3D scene rendering techniques such as Gaussian Splatting (GS) remains challenging. Existing models use additional meshing mechanisms, including triangle or tetrahedron meshing, marching cubes, or cage meshes. Alternatively, we can modify the physics-grounded Newtonian dynamics to align with 3D Gaussian components. Current models take the first-order approximation of a deformation map, which locally approximates the dynamics by linear transformations. In contrast, our GS for Physics-Based Simulations (GASP) pipeline uses parametrized flat Gaussian distributions. Consequently, the problem of modeling Gaussian components using the physics engine is reduced to working with 3D points. In our work, we present additional rules for manipulating Gaussians, demonstrating how to adapt the pipeline to incorporate meshes, control Gaussian sizes during simulations, and enhance simulation efficiency. This is achieved through the Gaussian grouping strategy, which implements hierarchical structuring and enables simulations to be performed exclusively on selected Gaussians. The resulting solution can be integrated into any physics engine that can be treated as a black box. As demonstrated in our studies, the proposed pipeline exhibits superior performance on a diverse range of benchmark datasets designed for 3D object rendering. The project webpage, which includes additional visualizations, can be found at https://waczjoan.github.io/GASP.

Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power. Data-driven methods based on large-scale machine learning promise high adaptivity by integrating long-range dependencies more directly and efficiently. In this work, we focus on fluid dynamics and address the shortcomings of a large part of the literature, which are based on fixed support for computations and predictions in the form of regular or irregular grids. We propose a novel setup to perform predictions in a continuous spatial and temporal domain while being trained on sparse observations. We formulate the task as a double observation problem and propose a solution with two interlinked dynamical systems defined on, respectively, the sparse positions and the continuous domain, which allows to forecast and interpolate a solution from the initial condition. Our practical implementation involves recurrent GNNs and a spatio-temporal attention observer capable of interpolating the solution at arbitrary locations. Our model not only generalizes to new initial conditions (as standard auto-regressive models do) but also performs evaluation at arbitrary space and time locations. We evaluate on three standard datasets in fluid dynamics and compare to strong baselines, which are outperformed both in classical settings and in the extended new task requiring continuous predictions.

Machine learning has emerged as a powerful solution to the modern challenges in accelerator physics. However, the limited availability of beam time, the computational cost of simulations, and the high-dimensionality of optimisation problems pose significant challenges in generating the required data for training state-of-the-art machine learning models. In this work, we introduce Cheetah, a PyTorch-based high-speed differentiable linear-beam dynamics code. Cheetah enables the fast collection of large data sets by reducing computation times by multiple orders of magnitude and facilitates efficient gradient-based optimisation for accelerator tuning and system identification. This positions Cheetah as a user-friendly, readily extensible tool that integrates seamlessly with widely adopted machine learning tools. We showcase the utility of Cheetah through five examples, including reinforcement learning training, gradient-based beamline tuning, gradient-based system identification, physics-informed Bayesian optimisation priors, and modular neural network surrogate modelling of space charge effects. The use of such a high-speed differentiable simulation code will simplify the development of machine learning-based methods for particle accelerators and fast-track their integration into everyday operations of accelerator facilities.

Adjusting and deforming 3D garments to body shapes, body motion, and cloth material is an important problem in virtual and augmented reality. Applications are numerous, ranging from virtual change rooms to the entertainment and gaming industry. This problem is challenging as garment dynamics influence geometric details such as wrinkling patterns, which depend on physical input including the wearer's body shape and motion, as well as cloth material features. Existing work studies learning-based modeling techniques to generate garment deformations from example data, and physics-inspired simulators to generate realistic garment dynamics. We propose here a learning-based approach trained on data generated with a physics-based simulator. Compared to prior work, our 3D generative model learns garment deformations for loose cloth geometry, especially for large deformations and dynamic wrinkles driven by body motion and cloth material. Furthermore, the model can be efficiently fitted to observations captured using vision sensors. We propose to leverage the capability of diffusion models to learn fine-scale detail: we model the 3D garment in a 2D parameter space, and learn a latent diffusion model using this representation independent from the mesh resolution. This allows to condition global and local geometric information with body and material information. We quantitatively and qualitatively evaluate our method on both simulated data and data captured with a multi-view acquisition platform. Compared to strong baselines, our method is more accurate in terms of Chamfer distance.

Existing video generation models excel at producing photo-realistic videos from text or images, but often lack physical plausibility and 3D controllability. To overcome these limitations, we introduce PhysCtrl, a novel framework for physics-grounded image-to-video generation with physical parameters and force control. At its core is a generative physics network that learns the distribution of physical dynamics across four materials (elastic, sand, plasticine, and rigid) via a diffusion model conditioned on physics parameters and applied forces. We represent physical dynamics as 3D point trajectories and train on a large-scale synthetic dataset of 550K animations generated by physics simulators. We enhance the diffusion model with a novel spatiotemporal attention block that emulates particle interactions and incorporates physics-based constraints during training to enforce physical plausibility. Experiments show that PhysCtrl generates realistic, physics-grounded motion trajectories which, when used to drive image-to-video models, yield high-fidelity, controllable videos that outperform existing methods in both visual quality and physical plausibility. Project Page: https://cwchenwang.github.io/physctrl

Data-driven approaches have revolutionized 3D vision, enabling transformers to effectively reconstruct and generate static 3D objects. However, generating simulative 4D dynamics -- realistic temporal deformations of static objects under various physical conditions -- remains challenging and often ad hoc, despite its importance in building comprehensive 3D world models. Most existing methods assume a predefined physical model and use system identification to estimate parameters, restricting these methods to specific categories and small-scale datasets. We propose that these restrictions can be overcome by learning a data-driven kinematic state parameterization for object-centric physical systems. Specifically, we learn both a latent space representing all possible states of the object and a decoder that maps any sampled latent to a plausibly deformed shape of the object. We refer to this parameterization as Neural Object Kinematics (NeuROK), and learn a transformer-based encoder-decoder model on a curated large-scale 4D dataset. This formulation and the learned model significantly simplify the generation of simulative dynamics since we only need to consider the dynamics within a low-dimensional latent space from the Lagrangian mechanics' perspective in classical physics. We demonstrate the effectiveness and generality of this neural simulation framework across diverse dynamic object types, showing clear advantages over prior works. Project page: https://chen-geng.com/neurok

Scene representations using 3D Gaussian primitives have produced excellent results in modeling the appearance of static and dynamic 3D scenes. Many graphics applications, however, demand the ability to manipulate both the appearance and the physical properties of objects. We introduce Feature Splatting, an approach that unifies physics-based dynamic scene synthesis with rich semantics from vision language foundation models that are grounded by natural language. Our first contribution is a way to distill high-quality, object-centric vision-language features into 3D Gaussians, that enables semi-automatic scene decomposition using text queries. Our second contribution is a way to synthesize physics-based dynamics from an otherwise static scene using a particle-based simulator, in which material properties are assigned automatically via text queries. We ablate key techniques used in this pipeline, to illustrate the challenge and opportunities in using feature-carrying 3D Gaussians as a unified format for appearance, geometry, material properties and semantics grounded on natural language. Project website: https://feature-splatting.github.io/

Physical principles are fundamental to realistic visual simulation, but remain a significant oversight in transformer-based video generation. This gap highlights a critical limitation in rendering rigid body motion, a core tenet of classical mechanics. While computer graphics and physics-based simulators can easily model such collisions using Newton formulas, modern pretrain-finetune paradigms discard the concept of object rigidity during pixel-level global denoising. Even perfectly correct mathematical constraints are treated as suboptimal solutions (i.e., conditions) during model optimization in post-training, fundamentally limiting the physical realism of generated videos. Motivated by these considerations, we introduce, for the first time, a physics-aware reinforcement learning paradigm for video generation models that enforces physical collision rules directly in high-dimensional spaces, ensuring the physics knowledge is strictly applied rather than treated as conditions. Subsequently, we extend this paradigm to a unified framework, termed Mimicry-Discovery Cycle (MDcycle), which allows substantial fine-tuning while fully preserving the model's ability to leverage physics-grounded feedback. To validate our approach, we construct new benchmark PhysRVGBench and perform extensive qualitative and quantitative experiments to thoroughly assess its effectiveness.

Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike favorable trade-offs between accuracy and efficiency. However, high-dimensional scientific simulations are very expensive to run, and solvers and parameters must often be tuned individually to each system studied. Here we introduce MeshGraphNets, a framework for learning mesh-based simulations using graph neural networks. Our model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation. Our results show it can accurately predict the dynamics of a wide range of physical systems, including aerodynamics, structural mechanics, and cloth. The model's adaptivity supports learning resolution-independent dynamics and can scale to more complex state spaces at test time. Our method is also highly efficient, running 1-2 orders of magnitude faster than the simulation on which it is trained. Our approach broadens the range of problems on which neural network simulators can operate and promises to improve the efficiency of complex, scientific modeling tasks.

We propose a neural physics system for real-time, interactive fluid simulations. Traditional physics-based methods, while accurate, are computationally intensive and suffer from latency issues. Recent machine-learning methods reduce computational costs while preserving fidelity; yet most still fail to satisfy the latency constraints for real-time use and lack support for interactive applications. To bridge this gap, we introduce a novel hybrid method that integrates numerical simulation, neural physics, and generative control. Our neural physics jointly pursues low-latency simulation and high physical fidelity by employing a fallback safeguard to classical numerical solvers. Furthermore, we develop a diffusion-based controller that is trained using a reverse modeling strategy to generate external dynamic force fields for fluid manipulation. Our system demonstrates robust performance across diverse 2D/3D scenarios, material types, and obstacle interactions, achieving real-time simulations at high frame rates (11~29% latency) while enabling fluid control guided by user-friendly freehand sketches. We present a significant step towards practical, controllable, and physically plausible fluid simulations for real-time interactive applications. We promise to release both models and data upon acceptance.

Interactive world models that simulate object dynamics are crucial for robotics, VR, and AR. However, it remains a significant challenge to learn physics-consistent dynamics models from limited real-world video data, especially for deformable objects with spatially-varying physical properties. To overcome the challenge of data scarcity, we propose PhysWorld, a novel framework that utilizes a simulator to synthesize physically plausible and diverse demonstrations to learn efficient world models. Specifically, we first construct a physics-consistent digital twin within MPM simulator via constitutive model selection and global-to-local optimization of physical properties. Subsequently, we apply part-aware perturbations to the physical properties and generate various motion patterns for the digital twin, synthesizing extensive and diverse demonstrations. Finally, using these demonstrations, we train a lightweight GNN-based world model that is embedded with physical properties. The real video can be used to further refine the physical properties. PhysWorld achieves accurate and fast future predictions for various deformable objects, and also generalizes well to novel interactions. Experiments show that PhysWorld has competitive performance while enabling inference speeds 47 times faster than the recent state-of-the-art method, i.e., PhysTwin.

Neural surrogates promise large speedups over classical solvers for physical dynamics but fail silently at sharp dynamical events such as shocks, fronts, and contact. We present hybrid neural world models for physical dynamics: a recipe for training and deploying multi-horizon surrogates in physical state space, where a single network with continuous horizon conditioning is trained with direct supervision against textbook reference solvers to predict any future state at horizon T in one forward pass. Although no part of the training data, loss function, or architecture supervises discontinuity location, the trained surrogate encodes it implicitly, recoverable from its forward passes alone as a per-trajectory error map that concentrates on shocks, fronts, and contacts, and stays small elsewhere. The map is competitive with or better than standard label-free baselines including deep ensembles, learned error heads, gradient-magnitude indicators, and locally-adaptive conformal prediction, while using only a single trained network and requiring no calibration set or governing-equation knowledge. The recipe supports two operating points. Mode 1 runs the surrogate alone for maximum throughput, with same-hardware CPU speedups of 26x to 72x against textbook solvers on the PDE environments. Mode 2 uses the error map to gate a reference-solver fallback, deferring uncertain trajectories and roughly halving the surrogate's residual error at the default operating point. The recipe applies without modification across reaction-diffusion, compressible Euler, and rigid-body collision dynamics.

Realistic simulation is critical for applications ranging from robotics to animation. Traditional analytic simulators sometimes struggle to capture sufficiently realistic simulation which can lead to problems including the well known "sim-to-real" gap in robotics. Learned simulators have emerged as an alternative for better capturing real-world physical dynamics, but require access to privileged ground truth physics information such as precise object geometry or particle tracks. Here we propose a method for learning simulators directly from observations. Visual Particle Dynamics (VPD) jointly learns a latent particle-based representation of 3D scenes, a neural simulator of the latent particle dynamics, and a renderer that can produce images of the scene from arbitrary views. VPD learns end to end from posed RGB-D videos and does not require access to privileged information. Unlike existing 2D video prediction models, we show that VPD's 3D structure enables scene editing and long-term predictions. These results pave the way for downstream applications ranging from video editing to robotic planning.

Video generation models have emerged as high-fidelity models of the physical world, capable of synthesizing high-quality videos capturing fine-grained interactions between agents and their environments conditioned on multi-modal user inputs. Their impressive capabilities address many of the long-standing challenges faced by physics-based simulators, driving broad adoption in many problem domains, e.g., robotics. For example, video models enable photorealistic, physically consistent deformable-body simulation without making prohibitive simplifying assumptions, which is a major bottleneck in physics-based simulation. Moreover, video models can serve as foundation world models that capture the dynamics of the world in a fine-grained and expressive way. They thus overcome the limited expressiveness of language-only abstractions in describing intricate physical interactions. In this survey, we provide a review of video models and their applications as embodied world models in robotics, encompassing cost-effective data generation and action prediction in imitation learning, dynamics and rewards modeling in reinforcement learning, visual planning, and policy evaluation. Further, we highlight important challenges hindering the trustworthy integration of video models in robotics, which include poor instruction following, hallucinations such as violations of physics, and unsafe content generation, in addition to fundamental limitations such as significant data curation, training, and inference costs. We present potential future directions to address these open research challenges to motivate research and ultimately facilitate broader applications, especially in safety-critical settings.

In recent years, there has been rapid development in 3D generation models, opening up new possibilities for applications such as simulating the dynamic movements of 3D objects and customizing their behaviors. However, current 3D generative models tend to focus only on surface features such as color and shape, neglecting the inherent physical properties that govern the behavior of objects in the real world. To accurately simulate physics-aligned dynamics, it is essential to predict the physical properties of materials and incorporate them into the behavior prediction process. Nonetheless, predicting the diverse materials of real-world objects is still challenging due to the complex nature of their physical attributes. In this paper, we propose Physics3D, a novel method for learning various physical properties of 3D objects through a video diffusion model. Our approach involves designing a highly generalizable physical simulation system based on a viscoelastic material model, which enables us to simulate a wide range of materials with high-fidelity capabilities. Moreover, we distill the physical priors from a video diffusion model that contains more understanding of realistic object materials. Extensive experiments demonstrate the effectiveness of our method with both elastic and plastic materials. Physics3D shows great potential for bridging the gap between the physical world and virtual neural space, providing a better integration and application of realistic physical principles in virtual environments. Project page: https://liuff19.github.io/Physics3D.

Video generation models have achieved remarkable progress in creating high-quality, photorealistic content. However, their ability to accurately simulate physical phenomena remains a critical and unresolved challenge. This paper presents PhyWorldBench, a comprehensive benchmark designed to evaluate video generation models based on their adherence to the laws of physics. The benchmark covers multiple levels of physical phenomena, ranging from fundamental principles like object motion and energy conservation to more complex scenarios involving rigid body interactions and human or animal motion. Additionally, we introduce a novel ""Anti-Physics"" category, where prompts intentionally violate real-world physics, enabling the assessment of whether models can follow such instructions while maintaining logical consistency. Besides large-scale human evaluation, we also design a simple yet effective method that could utilize current MLLM to evaluate the physics realism in a zero-shot fashion. We evaluate 12 state-of-the-art text-to-video generation models, including five open-source and five proprietary models, with a detailed comparison and analysis. we identify pivotal challenges models face in adhering to real-world physics. Through systematic testing of their outputs across 1,050 curated prompts-spanning fundamental, composite, and anti-physics scenarios-we identify pivotal challenges these models face in adhering to real-world physics. We then rigorously examine their performance on diverse physical phenomena with varying prompt types, deriving targeted recommendations for crafting prompts that enhance fidelity to physical principles.

Data-driven learning approaches for physics simulation, sometimes referred to as world models, have emerged as promising alternatives to traditional physics simulators due to their differentiable nature. Prior work has demonstrated impressive results in predicting the motions of rigid and non-rigid objects in complex scenes involving multiple interacting bodies. However, these models are typically trained in simulated environments because obtaining perfect state information such as complete scene point clouds and point correspondences over time is challenging in real-world settings. This reliance on synthetic data can limit their applicability when the sim-to-real gap is large. In this work, we aim to overcome these limitations by introducing a novel framework for training neural object dynamics models directly from unlabeled real-world videos. Specifically, we propose to learn a particle-based dynamics model compatible with a Gaussian splatting framework, which operates on dense particles derived from Gaussians (i.e., particles with scales and rotations) and predicts their position and rotation changes over time. The model is trained via rendering supervision, enabling learning from real-world videos without requiring particle-level labeled states. Our model operates directly on dense Gaussians without relying on heuristic subsampling anchor points. To enable this study, we also present a real-world dataset consisting of about 500 videos capturing diverse object interactions.

Modeling the dynamics of deformable objects is challenging due to their diverse physical properties and the difficulty of estimating states from limited visual information. We address these challenges with a neural dynamics framework that combines object particles and spatial grids in a hybrid representation. Our particle-grid model captures global shape and motion information while predicting dense particle movements, enabling the modeling of objects with varied shapes and materials. Particles represent object shapes, while the spatial grid discretizes the 3D space to ensure spatial continuity and enhance learning efficiency. Coupled with Gaussian Splattings for visual rendering, our framework achieves a fully learning-based digital twin of deformable objects and generates 3D action-conditioned videos. Through experiments, we demonstrate that our model learns the dynamics of diverse objects -- such as ropes, cloths, stuffed animals, and paper bags -- from sparse-view RGB-D recordings of robot-object interactions, while also generalizing at the category level to unseen instances. Our approach outperforms state-of-the-art learning-based and physics-based simulators, particularly in scenarios with limited camera views. Furthermore, we showcase the utility of our learned models in model-based planning, enabling goal-conditioned object manipulation across a range of tasks. The project page is available at https://kywind.github.io/pgnd .

Recent works exploring deep learning application to dynamical systems modeling have demonstrated that embedding physical priors into neural networks can yield more effective, physically-realistic, and data-efficient models. However, in the absence of complete prior knowledge of a dynamical system's physical characteristics, determining the optimal structure and optimization strategy for these models can be difficult. In this work, we explore methods for discovering neural state space dynamics models for system identification. Starting with a design space of block-oriented state space models and structured linear maps with strong physical priors, we encode these components into a model genome alongside network structure, penalty constraints, and optimization hyperparameters. Demonstrating the overall utility of the design space, we employ an asynchronous genetic search algorithm that alternates between model selection and optimization and obtains accurate physically consistent models of three physical systems: an aerodynamics body, a continuous stirred tank reactor, and a two tank interacting system.

Achieving spatial intelligence requires moving beyond visual plausibility to build world simulators grounded in physical laws. While coding LLMs have advanced static 3D scene generation, extending this paradigm to 4D dynamics remains a critical frontier. This task presents two fundamental challenges: multi-scale context entanglement, where monolithic generation fails to balance local object structures with global environmental layouts; and a semantic-physical execution gap, where open-loop code generation leads to physical hallucinations lacking dynamic fidelity. We introduce Code2Worlds, a framework that formulates 4D generation as language-to-simulation code generation. First, we propose a dual-stream architecture that disentangles retrieval-augmented object generation from hierarchical environmental orchestration. Second, to ensure dynamic fidelity, we establish a physics-aware closed-loop mechanism in which a PostProcess Agent scripts dynamics, coupled with a VLM-Motion Critic that performs self-reflection to iteratively refine simulation code. Evaluations on the Code4D benchmark show Code2Worlds outperforms baselines with a 41% SGS gain and 49% higher Richness, while uniquely generating physics-aware dynamics absent in prior static methods. Code: https://github.com/AIGeeksGroup/Code2Worlds. Website: https://aigeeksgroup.github.io/Code2Worlds.

Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh correspond to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods. Our code is available at https://github.com/yuyudeep/hcmt.

We present a self-supervised framework for learning implicit 3D physical dynamics directly from video-derived supervisory signals. While current generative video models achieve high visual fidelity, they lack a 3D geometric foundation, often resulting in physical inconsistencies and a failure to maintain object permanence. We address this by shifting the predictive bottleneck from 2D image space to a `lifted' 3D Volumetric Latent Space. Our method unprojects semantic features from a Video Joint-Embedding Predictive Architecture (V-JEPA) into a voxelized grid, grounded by monocular depth priors. This lifting enables a Volumetric Feature Advection to learn an action-conditioned transition operator that treats physics as a spatio-temporal state advection problem, i.e., learn implicit 3D physics. Unlike state-of-the-art hybrid models that rely on explicit classical simulators for training and/or inference, our architecture tracks material states implicitly within high-dimensional V-JEPA features. This allows for the emergent simulation of heterogeneous phenomena (e.g., rigid body motion in fluid flow) within a single, unified pipeline. Supervised solely via end-to-end video-derived signal plus action conditions, without access to physics engine internal states, labels, or surrogate models, our model demonstrates good long-term structural stability and physical plausibility on multiple benchmarks (CLEVERER, PhysInOne, PhysGaia). We believe that this work opens a scalable pathway toward general-purpose dynamic world models that internalize the 3D invariants of the physical world solely through passive observation of monocular videos.

This study investigates the application of deep residual networks for predicting the dynamics of interacting three-dimensional rigid bodies. We present a framework combining a 3D physics simulator implemented in C++ with a deep learning model constructed using PyTorch. The simulator generates training data encompassing linear and angular motion, elastic collisions, fluid friction, gravitational effects, and damping. Our deep residual network, consisting of an input layer, multiple residual blocks, and an output layer, is designed to handle the complexities of 3D dynamics. We evaluate the network's performance using a datasetof 10,000 simulated scenarios, each involving 3-5 interacting rigid bodies. The model achieves a mean squared error of 0.015 for position predictions and 0.022 for orientation predictions, representing a 25% improvement over baseline methods. Our results demonstrate the network's ability to capture intricate physical interactions, with particular success in predicting elastic collisions and rotational dynamics. This work significantly contributes to physics-informed machine learning by showcasing the immense potential of deep residual networks in modeling complex 3D physical systems. We discuss our approach's limitations and propose future directions for improving generalization to more diverse object shapes and materials.

Neural simulators promise efficient surrogates for physics simulation, but scaling them is bottlenecked by the prohibitive cost of generating high-fidelity training data. Pre-training on abundant off-the-shelf geometries offers a natural alternative, yet faces a fundamental gap: supervision on static geometry alone ignores dynamics and can lead to negative transfer on physics tasks. We present GeoPT, a unified pre-trained model for general physics simulation based on lifted geometric pre-training. The core idea is to augment geometry with synthetic dynamics, enabling dynamics-aware self-supervision without physics labels. Pre-trained on over one million samples, GeoPT consistently improves industrial-fidelity benchmarks spanning fluid mechanics for cars, aircraft, and ships, and solid mechanics in crash simulation, reducing labeled data requirements by 20-60% and accelerating convergence by 2times. These results show that lifting with synthetic dynamics bridges the geometry-physics gap, unlocking a scalable path for neural simulation and potentially beyond. Code is available at https://github.com/Physics-Scaling/GeoPT.

Mimicking realistic dynamics in 3D garment animations is a challenging task due to the complex nature of multi-layered garments and the variety of outer forces involved. Existing approaches mostly focus on single-layered garments driven by only human bodies and struggle to handle general scenarios. In this paper, we propose a novel data-driven method, called LayersNet, to model garment-level animations as particle-wise interactions in a micro physics system. We improve simulation efficiency by representing garments as patch-level particles in a two-level structural hierarchy. Moreover, we introduce a novel Rotation Equivalent Transformation that leverages the rotation invariance and additivity of physics systems to better model outer forces. To verify the effectiveness of our approach and bridge the gap between experimental environments and real-world scenarios, we introduce a new challenging dataset, D-LAYERS, containing 700K frames of dynamics of 4,900 different combinations of multi-layered garments driven by both human bodies and randomly sampled wind. Our experiments show that LayersNet achieves superior performance both quantitatively and qualitatively. We will make the dataset and code publicly available at https://mmlab-ntu.github.io/project/layersnet/index.html .

Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our framework---which we term "Graph Network-based Simulators" (GNS)---represents the state of a physical system with particles, expressed as nodes in a graph, and computes dynamics via learned message-passing. Our results show that our model can generalize from single-timestep predictions with thousands of particles during training, to different initial conditions, thousands of timesteps, and at least an order of magnitude more particles at test time. Our model was robust to hyperparameter choices across various evaluation metrics: the main determinants of long-term performance were the number of message-passing steps, and mitigating the accumulation of error by corrupting the training data with noise. Our GNS framework advances the state-of-the-art in learned physical simulation, and holds promise for solving a wide range of complex forward and inverse problems.

Predicting the dynamics of interacting objects is essential for both humans and intelligent systems. However, existing approaches are limited to simplified, toy settings and lack generalizability to complex, real-world environments. Recent advances in generative models have enabled the prediction of state transitions based on interventions, but focus on generating a single future state which neglects the continuous dynamics resulting from the interaction. To address this gap, we propose InterDyn, a novel framework that generates videos of interactive dynamics given an initial frame and a control signal encoding the motion of a driving object or actor. Our key insight is that large video generation models can act as both neural renderers and implicit physics ``simulators'', having learned interactive dynamics from large-scale video data. To effectively harness this capability, we introduce an interactive control mechanism that conditions the video generation process on the motion of the driving entity. Qualitative results demonstrate that InterDyn generates plausible, temporally consistent videos of complex object interactions while generalizing to unseen objects. Quantitative evaluations show that InterDyn outperforms baselines that focus on static state transitions. This work highlights the potential of leveraging video generative models as implicit physics engines. Project page: https://interdyn.is.tue.mpg.de/

We introduce adversarial learning methods for data-driven generative modeling of the dynamics of n^{th}-order stochastic systems. Our approach builds on Generative Adversarial Networks (GANs) with generative model classes based on stable m-step stochastic numerical integrators. We introduce different formulations and training methods for learning models of stochastic dynamics based on observation of trajectory samples. We develop approaches using discriminators based on Maximum Mean Discrepancy (MMD), training protocols using conditional and marginal distributions, and methods for learning dynamic responses over different time-scales. We show how our approaches can be used for modeling physical systems to learn force-laws, damping coefficients, and noise-related parameters. The adversarial learning approaches provide methods for obtaining stable generative models for dynamic tasks including long-time prediction and developing simulations for stochastic systems.

In this paper, we propose a probabilistic physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM). The framework targets the inference of the characteristics and latent structure of nonlinear dynamical systems from measurement data, where exact inference of latent variables is typically intractable. A recently surfaced option pertains to leveraging variational inference to perform approximate inference. In such a scheme, transition and emission functions of the system are parameterized via feed-forward neural networks (deep generative models). However, due to the generalized and highly versatile formulation of neural network functions, the learned latent space often lacks physical interpretation and structured representation. To address this, we bridge physics-based state space models with Deep Markov Models, thus delivering a hybrid modeling framework for unsupervised learning and identification of nonlinear dynamical systems. The proposed framework takes advantage of the expressive power of deep learning, while retaining the driving physics of the dynamical system by imposing physics-driven restrictions on the side of the latent space. We demonstrate the benefits of such a fusion in terms of achieving improved performance on illustrative simulation examples and experimental case studies of nonlinear systems. Our results indicate that the physics-based models involved in the employed transition and emission functions essentially enforce a more structured and physically interpretable latent space, which is essential for enhancing and generalizing the predictive capabilities of deep learning-based models.

Learning to simulate complex physical systems from data has emerged as a promising way to overcome the limitations of traditional numerical solvers, which often require prohibitive computational costs for high-fidelity solutions. Recent Graph Neural Simulators (GNSs) accelerate simulations by learning dynamics on graph-structured data, yet often struggle to capture long-range interactions and suffer from error accumulation under autoregressive rollouts. To address these challenges, we propose Information-preserving Graph Neural Simulators (IGNS), a graph-based neural simulator built on the principles of Hamiltonian dynamics. This structure guarantees preservation of information across the graph, while extending to port-Hamiltonian systems allows the model to capture a broader class of dynamics, including non-conservative effects. IGNS further incorporates a warmup phase to initialize global context, geometric encoding to handle irregular meshes, and a multi-step training objective that facilitates PDE matching, where the trajectory produced by integrating the port-Hamiltonian core aligns with the ground-truth trajectory, thereby reducing rollout error. To evaluate these properties systematically, we introduce new benchmarks that target long-range dependencies and challenging external forcing scenarios. Across all tasks, IGNS consistently outperforms state-of-the-art GNSs, achieving higher accuracy and stability under challenging and complex dynamical systems. Our project page: https://thobotics.github.io/neural_pde_matching.

Generative machine learning methods, such as diffusion models and flow matching, have shown great potential in modeling complex system behaviors and building efficient surrogate models. However, these methods typically learn the underlying physics implicitly from data. We propose Physics-Based Flow Matching (PBFM), a novel generative framework that explicitly embeds physical constraints, both PDE residuals and algebraic relations, into the flow matching objective. We also introduce temporal unrolling at training time that improves the accuracy of the final, noise-free sample prediction. Our method jointly minimizes the flow matching loss and the physics-based residual loss without requiring hyperparameter tuning of their relative weights. Additionally, we analyze the role of the minimum noise level, sigma_{min}, in the context of physical constraints and evaluate a stochastic sampling strategy that helps to reduce physical residuals. Through extensive benchmarks on three representative PDE problems, we show that our approach yields up to an 8times more accurate physical residuals compared to FM, while clearly outperforming existing algorithms in terms of distributional accuracy. PBFM thus provides a principled and efficient framework for surrogate modeling, uncertainty quantification, and accelerated simulation in physics and engineering applications.

Body dynamics are crucial information for the analysis of human motions in important research fields, ranging from biomechanics, sports science to computer vision and graphics. Modern approaches collect the body dynamics, external reactive force specifically, via force plates, synchronizing with human motion capture data, and learn to estimate the dynamics from a black-box deep learning model. Being specialized devices, force plates can only be installed in laboratory setups, imposing a significant limitation on the learning of human dynamics. To this end, we propose a novel method for estimating human ground reaction dynamics directly from the more reliable motion capture data with physics laws and computational simulation as constrains. We introduce a highly accurate and robust method for computing ground reaction forces from motion capture data using Euler's integration scheme and PD algorithm. The physics-based reactive forces are used to inform the learning model about the physics-informed motion dynamics thus improving the estimation accuracy. The proposed approach was tested on the GroundLink dataset, outperforming the baseline model on: 1) the ground reaction force estimation accuracy compared to the force plates measurement; and 2) our simulated root trajectory precision. The implementation code is available at https://github.com/cuongle1206/Phys-GRD

Traditional fluid dynamics simulation pipelines combine numerical solvers with rendering, producing highly realistic results but at considerable computational cost. Diffusion-based generative video models offer a faster alternative, yet often ignore physical laws and thus fail to capture consistent dynamics. We propose a physics-informed video diffusion framework that jointly generates visual outputs and physical states. Unlike prior two-stage approaches that first simulate the physical variables and then render, we directly integrate physics constraints into the generative process, enabling simultaneous prediction of physical states and realistic videos without a separate rendering step. Built on the two-dimensional shallow water equations with terrain topography, our method produces temporally coherent water flow while maintaining physical plausibility. Experiments show that it outperforms purely data-driven video diffusion baselines in both realism and physical fidelity, while generating videos significantly faster than traditional simulation-plus-rendering pipelines.

Video generation models have shown strong potential as world models for autonomous driving simulation. However, existing approaches are primarily trained on real-world driving datasets, which mostly contain natural and safe driving scenarios. As a result, current models often fail when conditioned on challenging or counterfactual trajectories-such as imperfect trajectories generated by simulators or planning systems-producing videos with severe physical inconsistencies and artifacts. To address this limitation, we propose PhyGenesis, a world model designed to generate driving videos with high visual fidelity and strong physical consistency. Our framework consists of two key components: (1) a physical condition generator that transforms potentially invalid trajectory inputs into physically plausible conditions, and (2) a physics-enhanced video generator that produces high-fidelity multi-view driving videos under these conditions. To effectively train these components, we construct a large-scale, physics-rich heterogeneous dataset. Specifically, in addition to real-world driving videos, we generate diverse challenging driving scenarios using the CARLA simulator, from which we derive supervision signals that guide the model to learn physically grounded dynamics under extreme conditions. This challenging-trajectory learning strategy enables trajectory correction and promotes physically consistent video generation. Extensive experiments demonstrate that PhyGenesis consistently outperforms state-of-the-art methods, especially on challenging trajectories. Our project page is available at: https://wm-research.github.io/PhyGenesis/.

Foundation models have achieved remarkable success across video, image, and language domains. By scaling up the number of parameters and training datasets, these models acquire generalizable world knowledge and often surpass task-specific approaches. However, such progress has yet to extend to the domain of physics simulation. A primary bottleneck is data scarcity: while millions of images, videos, and textual resources are readily available on the internet, the largest physics simulation datasets contain only tens of thousands of samples. This data limitation hinders the use of large models, as overfitting becomes a major concern. As a result, physics applications typically rely on small models, which struggle with long-range prediction due to limited context understanding. Additionally, unlike images, videos, or text-which typically exhibit fixed granularity-physics datasets often vary drastically in scale, amplifying the challenges of scaling up multitask training. We introduce PhysiX, the first large-scale foundation model for physics simulation. PhysiX is a 4.5B parameter autoregressive generative model. It uses a discrete tokenizer to encode physical processes at different scales into a sequence of discrete tokens, and employs an autoregressive next-token prediction objective to model such processes in the token space. To mitigate the rounding error in the discretization process, PhysiX incorporates a specialized refinement module. Through extensive experiments, we show that PhysiX effectively addresses the data bottleneck, outperforming task-specific baselines under comparable settings as well as the previous absolute state-of-the-art approaches on The Well benchmark. Our results indicate that knowledge learned from natural videos can be successfully transferred to physics simulation, and that joint training across diverse simulation tasks enables synergistic learning.

Robotic manipulation with deformable objects represents a data-intensive regime in embodied learning, where shape, contact, and topology co-evolve in ways that far exceed the variability of rigids. Although simulation promises relief from the cost of real-world data acquisition, prevailing sim-to-real pipelines remain rooted in rigid-body abstractions, producing mismatched geometry, fragile soft dynamics, and motion primitives poorly suited for cloth interaction. We posit that simulation fails not for being synthetic, but for being ungrounded. To address this, we introduce SIM1, a physics-aligned real-to-sim-to-real data engine that grounds simulation in the physical world. Given limited demonstrations, the system digitizes scenes into metric-consistent twins, calibrates deformable dynamics through elastic modeling, and expands behaviors via diffusion-based trajectory generation with quality filtering. This pipeline transforms sparse observations into scaled synthetic supervision with near-demonstration fidelity. Experiments show that policies trained on purely synthetic data achieve parity with real-data baselines at a 1:15 equivalence ratio, while delivering 90% zero-shot success and 50% generalization gains in real-world deployment. These results validate physics-aligned simulation as scalable supervision for deformable manipulation and a practical pathway for data-efficient policy learning.

Realistic object interactions are crucial for creating immersive virtual experiences, yet synthesizing realistic 3D object dynamics in response to novel interactions remains a significant challenge. Unlike unconditional or text-conditioned dynamics generation, action-conditioned dynamics requires perceiving the physical material properties of objects and grounding the 3D motion prediction on these properties, such as object stiffness. However, estimating physical material properties is an open problem due to the lack of material ground-truth data, as measuring these properties for real objects is highly difficult. We present PhysDreamer, a physics-based approach that endows static 3D objects with interactive dynamics by leveraging the object dynamics priors learned by video generation models. By distilling these priors, PhysDreamer enables the synthesis of realistic object responses to novel interactions, such as external forces or agent manipulations. We demonstrate our approach on diverse examples of elastic objects and evaluate the realism of the synthesized interactions through a user study. PhysDreamer takes a step towards more engaging and realistic virtual experiences by enabling static 3D objects to dynamically respond to interactive stimuli in a physically plausible manner. See our project page at https://physdreamer.github.io/.

We present PhysInOne, a large-scale synthetic dataset addressing the critical scarcity of physically-grounded training data for AI systems. Unlike existing datasets limited to merely hundreds or thousands of examples, PhysInOne provides 2 million videos across 153,810 dynamic 3D scenes, covering 71 basic physical phenomena in mechanics, optics, fluid dynamics, and magnetism. Distinct from previous works, our scenes feature multiobject interactions against complex backgrounds, with comprehensive ground-truth annotations including 3D geometry, semantics, dynamic motion, physical properties, and text descriptions. We demonstrate PhysInOne's efficacy across four emerging applications: physics-aware video generation, long-/short-term future frame prediction, physical property estimation, and motion transfer. Experiments show that fine-tuning foundation models on PhysInOne significantly enhances physical plausibility, while also exposing critical gaps in modeling complex physical dynamics and estimating intrinsic properties. As the largest dataset of its kind, orders of magnitude beyond prior works, PhysInOne establishes a new benchmark for advancing physics-grounded world models in generation, simulation, and embodied AI.

Existing imitation learning (IL) methods such as inverse reinforcement learning (IRL) usually have a double-loop training process, alternating between learning a reward function and a policy and tend to suffer long training time and high variance. In this work, we identify the benefits of differentiable physics simulators and propose a new IL method, i.e., Imitation Learning via Differentiable Physics (ILD), which gets rid of the double-loop design and achieves significant improvements in final performance, convergence speed, and stability. The proposed ILD incorporates the differentiable physics simulator as a physics prior into its computational graph for policy learning. It unrolls the dynamics by sampling actions from a parameterized policy, simply minimizing the distance between the expert trajectory and the agent trajectory, and back-propagating the gradient into the policy via temporal physics operators. With the physics prior, ILD policies can not only be transferable to unseen environment specifications but also yield higher final performance on a variety of tasks. In addition, ILD naturally forms a single-loop structure, which significantly improves the stability and training speed. To simplify the complex optimization landscape induced by temporal physics operations, ILD dynamically selects the learning objectives for each state during optimization. In our experiments, we show that ILD outperforms state-of-the-art methods in a variety of continuous control tasks with Brax, requiring only one expert demonstration. In addition, ILD can be applied to challenging deformable object manipulation tasks and can be generalized to unseen configurations.

Transforming static images into interactive experiences remains a challenging task in computer vision. Tackling this challenge holds the potential to elevate mobile user experiences, notably through interactive and AR/VR applications. Current approaches aim to achieve this either using pre-recorded video responses or requiring multi-view images as input. In this paper, we present PhysID, that streamlines the creation of physics-based interactive dynamics from a single-view image by leveraging large generative models for 3D mesh generation and physical property prediction. This significantly reduces the expertise required for engineering-intensive tasks like 3D modeling and intrinsic property calibration, enabling the process to be scaled with minimal manual intervention. We integrate an on-device physics-based engine for physically plausible real-time rendering with user interactions. PhysID represents a leap forward in mobile-based interactive dynamics, offering real-time, non-deterministic interactions and user-personalization with efficient on-device memory consumption. Experiments evaluate the zero-shot capabilities of various Multimodal Large Language Models (MLLMs) on diverse tasks and the performance of 3D reconstruction models. These results demonstrate the cohesive functioning of all modules within the end-to-end framework, contributing to its effectiveness.

Recent advances in video generation have shown remarkable potential for constructing world simulators. However, current models still struggle to produce physically consistent results, particularly when handling large-scale or complex dynamics. This limitation arises primarily because existing approaches respond isotropically to physical prompts and neglect the fine-grained alignment between generated content and localized physical cues. To address these challenges, we propose ProPhy, a Progressive Physical Alignment Framework that enables explicit physics-aware conditioning and anisotropic generation. ProPhy employs a two-stage Mixture-of-Physics-Experts (MoPE) mechanism for discriminative physical prior extraction, where Semantic Experts infer semantic-level physical principles from textual descriptions, and Refinement Experts capture token-level physical dynamics. This mechanism allows the model to learn fine-grained, physics-aware video representations that better reflect underlying physical laws. Furthermore, we introduce a physical alignment strategy that transfers the physical reasoning capabilities of vision-language models (VLMs) into the Refinement Experts, facilitating a more accurate representation of dynamic physical phenomena. Extensive experiments on physics-aware video generation benchmarks demonstrate that ProPhy produces more realistic, dynamic, and physically coherent results than existing state-of-the-art methods.

Recent advances in generative video modeling, driven by large-scale datasets and powerful architectures, have yielded remarkable visual realism. However, emerging evidence suggests that simply scaling data and model size does not endow these systems with an understanding of the underlying physical laws that govern real-world dynamics. Existing approaches often fail to capture or enforce such physical consistency, resulting in unrealistic motion and dynamics. In his work, we investigate whether integrating the inference of latent physical properties directly into the video generation process can equip models with the ability to produce physically plausible videos. To this end, we propose Phantom, a Physics-Infused Video Generation model that jointly models the visual content and latent physical dynamics. Conditioned on observed video frames and inferred physical states, Phantom jointly predicts latent physical dynamics and generates future video frames. Phantom leverages a physics-aware video representation that serves as an abstract yet informaive embedding of the underlying physics, facilitating the joint prediction of physical dynamics alongside video content without requiring an explicit specification of a complex set of physical dynamics and properties. By integrating the inference of physical-aware video representation directly into the video generation process, Phantom produces video sequences that are both visually realistic and physically consistent. Quantitative and qualitative results on both standard video generation and physics-aware benchmarks demonstrate that Phantom not only outperforms existing methods in terms of adherence to physical dynamics but also delivers competitive perceptual fidelity.

While recent video generation models have achieved significant visual fidelity, they often suffer from the lack of explicit physical controllability and plausibility. To address this, some recent studies attempted to guide the video generation with physics-based rendering. However, these methods face inherent challenges in accurately modeling complex physical properties and effectively control ling the resulting physical behavior over extended temporal sequences. In this work, we introduce PhysChoreo, a novel framework that can generate videos with diverse controllability and physical realism from a single image. Our method consists of two stages: first, it estimates the static initial physical properties of all objects in the image through part-aware physical property reconstruction. Then, through temporally instructed and physically editable simulation, it synthesizes high-quality videos with rich dynamic behaviors and physical realism. Experimental results show that PhysChoreo can generate videos with rich behaviors and physical realism, outperforming state-of-the-art methods on multiple evaluation metrics.

Simulating physical systems governed by Lagrangian dynamics often entails solving partial differential equations (PDEs) over high-resolution spatial domains, leading to significant computational expense. Reduced-order modeling (ROM) mitigates this cost by evolving low-dimensional latent representations of the underlying system. While neural ROMs enable querying solutions from latent states at arbitrary spatial points, their latent states typically represent the global domain and struggle to capture localized, highly dynamic behaviors such as fluids. We propose a sampling-based reduction framework that evolves Lagrangian systems directly in physical space over the particles themselves, reducing the number of active degrees of freedom via data-driven neural PDE operators. To enable querying at arbitrary spatial locations, we introduce a learnable kernel parameterization that uses local spatial information from time-evolved sample particles to infer the underlying solution manifold. Empirically, our approach achieves a 6.6x to 32x reduction in input dimensionality while maintaining high-fidelity evaluations across diverse Lagrangian regimes, including fluid flows, granular media, and elastoplastic dynamics. We refer to this framework as GIOROM (Geometry-Informed Reduced-Order Modeling). All code and data are available at: https://github.com/HrishikeshVish/GIOROM

This paper tackles the problem of physics-aware human motion synthesis in a dynamic scene. Unlike existing works which mainly tend to generate physically unrealistic motions due to limited contact modeling, typically restricted to hands, in this paper, we introduce a physics-aware human motion generation framework that explicitly models the full spectrum of human-related forces, including human-object, human-scene, and internal body dynamics.~Our method imposes soft physical constraints to maintain force and torque balance, ensuring physically grounded motion synthesis. We further propose a novel continuous distance-based force model that generalizes contact modeling to arbitrary surfaces, capturing interactions not only with static environments but also with dynamic, moving objects. Extensive experiments show that our approach significantly improves physical plausibility and generalizes well to complex scenes, setting a new benchmark for physically consistent human motion generation.

Machine learning-based surrogate models have emerged as a powerful tool to accelerate simulation-driven scientific workflows. However, their widespread adoption is hindered by the lack of large-scale, diverse, and standardized datasets tailored to physics-based simulations. While existing initiatives provide valuable contributions, many are limited in scope-focusing on specific physics domains, relying on fragmented tooling, or adhering to overly simplistic datamodels that restrict generalization. To address these limitations, we introduce PLAID (Physics-Learning AI Datamodel), a flexible and extensible framework for representing and sharing datasets of physics simulations. PLAID defines a unified standard for describing simulation data and is accompanied by a library for creating, reading, and manipulating complex datasets across a wide range of physical use cases (gitlab.com/drti/plaid). We release six carefully crafted datasets under the PLAID standard, covering structural mechanics and computational fluid dynamics, and provide baseline benchmarks using representative learning methods. Benchmarking tools are made available on Hugging Face, enabling direct participation by the community and contribution to ongoing evaluation efforts (huggingface.co/PLAIDcompetitions).

An embodied system must not only model the patterns of the external world but also understand its own motion dynamics. A motion dynamic model is essential for efficient skill acquisition and effective planning. In this work, we introduce the neural motion simulator (MoSim), a world model that predicts the future physical state of an embodied system based on current observations and actions. MoSim achieves state-of-the-art performance in physical state prediction and provides competitive performance across a range of downstream tasks. This works shows that when a world model is accurate enough and performs precise long-horizon predictions, it can facilitate efficient skill acquisition in imagined worlds and even enable zero-shot reinforcement learning. Furthermore, MoSim can transform any model-free reinforcement learning (RL) algorithm into a model-based approach, effectively decoupling physical environment modeling from RL algorithm development. This separation allows for independent advancements in RL algorithms and world modeling, significantly improving sample efficiency and enhancing generalization capabilities. Our findings highlight that world models for motion dynamics is a promising direction for developing more versatile and capable embodied systems.

Motion planning under dynamics constraints, i.e., kinodynamic planning, enables safe robot operation by generating dynamically feasible trajectories that the robot can accurately track. For high-\dof robots such as manipulators, sampling-based motion planners are commonly used, especially for complex tasks in cluttered environments. However, enforcing constraints on robot dynamics in such planners requires solving either challenging two-point boundary value problems (BVPs) or propagating robot dynamics over time, both of which are computational bottlenecks that drastically increase planning times. Meanwhile, recent efforts have shown that sampling-based motion planners can generate plans in microseconds using parallelization, but are limited to geometric paths. This paper develops AkinoPDF, a fast parallelized sampling-based kinodynamic motion planning technique for a broad class of differentially flat robot systems, including manipulators, ground and aerial vehicles, and more. Differential flatness allows us to transform the motion planning problem from the original state space to a flat output space, where an analytical time-parameterized solution of the BVP and dynamics integration can be obtained. A trajectory in the flat output space is then converted back to a closed-form dynamically feasible trajectory in the original state space, enabling fast validation via ``single instruction, multiple data" parallelism. Our method is fast, exact, and compatible with any sampling-based motion planner. We extensively verify the effectiveness of our approach in both simulated benchmarks and real experiments with cluttered and dynamic environments, requiring mere microseconds to milliseconds of planning time.

We have witnessed remarkable advances in LLM reasoning capabilities with the advent of DeepSeek-R1. However, much of this progress has been fueled by the abundance of internet question-answer (QA) pairs, a major bottleneck going forward, since such data is limited in scale and concentrated mainly in domains like mathematics. In contrast, other sciences such as physics lack large-scale QA datasets to effectively train reasoning-capable models. In this work, we show that physics simulators can serve as a powerful alternative source of supervision for training LLMs for physical reasoning. We generate random scenes in physics engines, create synthetic question-answer pairs from simulated interactions, and train LLMs using reinforcement learning on this synthetic data. Our models exhibit zero-shot sim-to-real transfer to real-world physics benchmarks: for example, training solely on synthetic simulated data improves performance on IPhO (International Physics Olympiad) problems by 5-10 percentage points across model sizes. These results demonstrate that physics simulators can act as scalable data generators, enabling LLMs to acquire deep physical reasoning skills beyond the limitations of internet-scale QA data. Code available at: https://sim2reason.github.io/.

4D content generation focuses on creating dynamic 3D objects that change over time. Existing methods primarily rely on pre-trained video diffusion models, utilizing sampling processes or reference videos. However, these approaches face significant challenges. Firstly, the generated 4D content often fails to adhere to real-world physics since video diffusion models do not incorporate physical priors. Secondly, the extensive sampling process and the large number of parameters in diffusion models result in exceedingly time-consuming generation processes. To address these issues, we introduce Phy124, a novel, fast, and physics-driven method for controllable 4D content generation from a single image. Phy124 integrates physical simulation directly into the 4D generation process, ensuring that the resulting 4D content adheres to natural physical laws. Phy124 also eliminates the use of diffusion models during the 4D dynamics generation phase, significantly speeding up the process. Phy124 allows for the control of 4D dynamics, including movement speed and direction, by manipulating external forces. Extensive experiments demonstrate that Phy124 generates high-fidelity 4D content with significantly reduced inference times, achieving stateof-the-art performance. The code and generated 4D content are available at the provided link: https://anonymous.4open.science/r/BBF2/.

Time-domain simulations are crucial for ensuring power system stability and avoiding critical scenarios that could lead to blackouts. The next-generation power systems require a significant increase in the computational cost and complexity of these simulations due to additional degrees of uncertainty, non-linearity and states. Physics-Informed Neural Networks (PINN) have been shown to accelerate single-component simulations by several orders of magnitude. However, their application to current time-domain simulation solvers has been particularly challenging since the system's dynamics depend on multiple components. Using a new training formulation, this paper introduces the first natural step to integrate PINNs into multi-component time-domain simulations. We propose PINNs as an alternative to other classical numerical methods for individual components. Once trained, these neural networks approximate component dynamics more accurately for longer time steps. Formulated as an implicit and consistent method with the transient simulation workflow, PINNs speed up simulation time by significantly increasing the time steps used. For explanation clarity, we demonstrate the training, integration, and simulation framework for several combinations of PINNs and numerical solution methods using the IEEE 9-bus system, although the method applies equally well to any power system size.

Recent advances in diffusion-based video generation have achieved remarkable visual realism but still struggle to obey basic physical laws such as gravity, inertia, and collision. Generated objects often move inconsistently across frames, exhibit implausible dynamics, or violate physical constraints, limiting the realism and reliability of AI-generated videos. We address this gap by introducing Physical Simulator In-the-loop Video Generation (PSIVG), a novel framework that integrates a physical simulator into the video diffusion process. Starting from a template video generated by a pre-trained diffusion model, PSIVG reconstructs the 4D scene and foreground object meshes, initializes them within a physical simulator, and generates physically consistent trajectories. These simulated trajectories are then used to guide the video generator toward spatio-temporally physically coherent motion. To further improve texture consistency during object movement, we propose a Test-Time Texture Consistency Optimization (TTCO) technique that adapts text and feature embeddings based on pixel correspondences from the simulator. Comprehensive experiments demonstrate that PSIVG produces videos that better adhere to real-world physics while preserving visual quality and diversity. Project Page: https://vcai.mpi-inf.mpg.de/projects/PSIVG/

While instruction-based image editing, enabled by multi-modal generative models, has advanced significantly, existing benchmarks lack a comprehensive evaluation of physics-based reasoning, a critical capability for handling real-world scenarios. To address this, we introduce PhyEditBench, a benchmark designed to assess the physical understanding of editing models. Guided by a hierarchical taxonomy, we establish 4 primary classes and 12 subclasses. It comprises 238 high-quality, high-resolution, real-world instances meticulously extracted from videos to capture authentic physical dynamics, alongside 35 synthetic Anti-Physics instances. Our empirical analysis of current SOTA editing methods exposes substantial limitations in their physics-based reasoning. We further propose a training-free baseline named PhyWorld that uses test-time scaling and a latent reduction strategy. PhyWorld outperforms comparable models and suggests that the video generation process can effectively serve as a reasoning mechanism for image editing. The project page is available at https://github.com/Previsior/PhyEditBench.

Video Diffusion Models (VDMs) offer a promising approach for simulating dynamic scenes and environments, with broad applications in robotics and media generation. However, existing models often generate temporally incoherent content that violates basic physical intuition, significantly limiting their practical applicability. We propose PhysAlign, an efficient framework for physics-coherent image-to-video (I2V) generation that explicitly addresses this limitation. To overcome the critical scarcity of physics-annotated videos, we first construct a fully controllable synthetic data generation pipeline based on rigid-body simulation, yielding a highly-curated dataset with accurate, fine-grained physics and 3D annotations. Leveraging this data, PhysAlign constructs a unified physical latent space by coupling explicit 3D geometry constraints with a Gram-based spatio-temporal relational alignment that extracts kinematic priors from video foundation models. Extensive experiments demonstrate that PhysAlign significantly outperforms existing VDMs on tasks requiring complex physical reasoning and temporal stability, without compromising zero-shot visual quality. PhysAlign shows the potential to bridge the gap between raw visual synthesis and rigid-body kinematics, establishing a practical paradigm for genuinely physics-grounded video generation. The project page is available at https://physalign.github.io/PhysAlign.

Machine learning approaches to spatiotemporal physical systems have primarily focused on next-frame prediction, with the goal of learning an accurate emulator for the system's evolution in time. However, these emulators are computationally expensive to train and are subject to performance pitfalls, such as compounding errors during autoregressive rollout. In this work, we take a different perspective and look at scientific tasks further downstream of predicting the next frame, such as estimation of a system's governing physical parameters. Accuracy on these tasks offers a uniquely quantifiable glimpse into the physical relevance of the representations of these models. We evaluate the effectiveness of general-purpose self-supervised methods in learning physics-grounded representations that are useful for downstream scientific tasks. Surprisingly, we find that not all methods designed for physical modeling outperform generic self-supervised learning methods on these tasks, and methods that learn in the latent space (e.g., joint embedding predictive architectures, or JEPAs) outperform those optimizing pixel-level prediction objectives. Code is available at https://github.com/helenqu/physical-representation-learning.

Previous work has evaluated physics reasoning in foundation models using synthetic or semi-synthetic scenes and visual question-answering tasks. However, these benchmarks emphasize high-level events and lack the visual fidelity required to assess true low-level Newtonian understanding. We introduce NewtPhys, a 4D physically annotated dataset built from multiview images of real-world scenes with physics-grounded simulations. The dataset provides dense, fine-grained annotations across timesteps -- including 3D forces and amodal per-pixel quantities covering physics, tracking, semantics and geometry -- bridging the gap between simplistic synthetic setups and realistic visual complexity. Using NewtPhys, we systematically evaluate 56 VLMs, including 54 open-weight models and 2 closed-source frontier models, and 10 VFMs and reveal limitations in low-level physics reasoning. Beyond benchmarking, our dataset enables future research in physics-grounded vision and the development of next-generation physics-aware evaluations. Code and datasets are available at https://astra-vision.github.io/NewtPhys.

A primary bottleneck in large-scale text-to-video generation today is physical consistency and controllability. Despite recent advances, state-of-the-art models often produce unrealistic motions, such as objects falling upward, or abrupt changes in velocity and direction. Moreover, these models lack precise parameter control, struggling to generate physically consistent dynamics under different initial conditions. We argue that this fundamental limitation stems from current models learning motion distributions solely from appearance, while lacking an understanding of the underlying dynamics. In this work, we propose NewtonGen, a framework that integrates data-driven synthesis with learnable physical principles. At its core lies trainable Neural Newtonian Dynamics (NND), which can model and predict a variety of Newtonian motions, thereby injecting latent dynamical constraints into the video generation process. By jointly leveraging data priors and dynamical guidance, NewtonGen enables physically consistent video synthesis with precise parameter control.

World simulators can provide safe and scalable environments for training Physical AI systems before real-world deployment. Large video generation models are emerging as a promising basis for such simulators because they can generate diverse and realistic visual futures. However, using them as world simulators requires physically faithful video continuations, namely, generated videos that preserve the physical state implied by the conditioning input, and evolve in ways consistent with basic physical principles. We propose PhyWorld, a video generation world model designed to produce temporally coherent and physically faithful scene continuations through two-stage post-training. In the first stage, we improve video-to-video continuation with flow matching fine-tuning, encouraging stable visual attributes and coherent motion dynamics across frames. In the second stage, we align generated dynamics with physical principles using Direct Preference Optimization (DPO) over physics preference pairs, guiding the model toward outputs with higher physical plausibility. To evaluate PhyWorld, we use both standard video-quality benchmarks and a dedicated physical-faithfulness benchmark with per-law scoring. Experiments show that PhyWorld improves video consistency, achieving an average score of 0.769 on VBench compared with 0.756 or below for state-of-the-art baselines. PhyWorld also improves physical plausibility, reaching an average score of 3.09 on our physical-faithfulness benchmark compared with 2.99 for the strongest baseline. These results suggest that post-training large video generation models with continuation and physics-preference signals can make them more effective world simulators for Physical AI.

OpenAI's Sora highlights the potential of video generation for developing world models that adhere to fundamental physical laws. However, the ability of video generation models to discover such laws purely from visual data without human priors can be questioned. A world model learning the true law should give predictions robust to nuances and correctly extrapolate on unseen scenarios. In this work, we evaluate across three key scenarios: in-distribution, out-of-distribution, and combinatorial generalization. We developed a 2D simulation testbed for object movement and collisions to generate videos deterministically governed by one or more classical mechanics laws. This provides an unlimited supply of data for large-scale experimentation and enables quantitative evaluation of whether the generated videos adhere to physical laws. We trained diffusion-based video generation models to predict object movements based on initial frames. Our scaling experiments show perfect generalization within the distribution, measurable scaling behavior for combinatorial generalization, but failure in out-of-distribution scenarios. Further experiments reveal two key insights about the generalization mechanisms of these models: (1) the models fail to abstract general physical rules and instead exhibit "case-based" generalization behavior, i.e., mimicking the closest training example; (2) when generalizing to new cases, models are observed to prioritize different factors when referencing training data: color > size > velocity > shape. Our study suggests that scaling alone is insufficient for video generation models to uncover fundamental physical laws, despite its role in Sora's broader success. See our project page at https://phyworld.github.io

Recent advancements in video generation have enabled the development of ``world models'' capable of simulating potential futures for robotics and planning. However, specifying precise goals for these models remains a challenge; text instructions are often too abstract to capture physical nuances, while target images are frequently infeasible to specify for dynamic tasks. To address this, we introduce Goal Force, a novel framework that allows users to define goals via explicit force vectors and intermediate dynamics, mirroring how humans conceptualize physical tasks. We train a video generation model on a curated dataset of synthetic causal primitives-such as elastic collisions and falling dominos-teaching it to propagate forces through time and space. Despite being trained on simple physics data, our model exhibits remarkable zero-shot generalization to complex, real-world scenarios, including tool manipulation and multi-object causal chains. Our results suggest that by grounding video generation in fundamental physical interactions, models can emerge as implicit neural physics simulators, enabling precise, physics-aware planning without reliance on external engines. We release all datasets, code, model weights, and interactive video demos at our project page.

Generative world models are increasingly used for video generation, where learned simulators are expected to capture the physical rules that govern real-world dynamics. However, evaluating whether generated videos actually follow these rules remains challenging. Existing physics-focused video benchmarks have made important progress, but they still face three key challenges, including the coarse evaluation frameworks that hide law-specific failures, response biases and fatigue that undermine the validity of annotation judgments, and automated evaluators that are insufficiently physics-aware or difficult to audit. To address those challenges, we introduce PhyGround, a criteria-grounded benchmark for evaluating physical reasoning in video generation. The benchmark contains 250 curated prompts, each augmented with an expected physical outcome, and a taxonomy of 13 physical laws across solid-body mechanics, fluid dynamics, and optics. Each law is operationalized through observable sub-questions to enable per-law diagnostics. We evaluate eight modern video generation models through a large-scale, quality-controlled human study, grounded on social science lab experiment design. A total of 459 annotators provided 5,796 complete annotations and over 37.4K fine-grained labels; after quality control, the retained annotations exhibited high split-half model-ranking correlations (Spearman's rho > 0.90). To support reproducible automated evaluation, we release PhyJudge-9B, an open physics-specialized VLM judge. PhyJudge-9B achieves substantially lower aggregate relative bias than Gemini-3.1-Pro (3.3% vs. 16.6%). We release prompts, human annotations, model checkpoints, and evaluation code on the project page https://phyground.github.io/.

Recent advances in video generation models have sparked interest in world models capable of simulating realistic environments. While navigation has been well-explored, physically meaningful interactions that mimic real-world forces remain largely understudied. In this work, we investigate using physical forces as a control signal for video generation and propose force prompts which enable users to interact with images through both localized point forces, such as poking a plant, and global wind force fields, such as wind blowing on fabric. We demonstrate that these force prompts can enable videos to respond realistically to physical control signals by leveraging the visual and motion prior in the original pretrained model, without using any 3D asset or physics simulator at inference. The primary challenge of force prompting is the difficulty in obtaining high quality paired force-video training data, both in the real world due to the difficulty of obtaining force signals, and in synthetic data due to limitations in the visual quality and domain diversity of physics simulators. Our key finding is that video generation models can generalize remarkably well when adapted to follow physical force conditioning from videos synthesized by Blender, even with limited demonstrations of few objects. Our method can generate videos which simulate forces across diverse geometries, settings, and materials. We also try to understand the source of this generalization and perform ablations that reveal two key elements: visual diversity and the use of specific text keywords during training. Our approach is trained on only around 15k training examples for a single day on four A100 GPUs, and outperforms existing methods on force adherence and physics realism, bringing world models closer to real-world physics interactions. We release all datasets, code, weights, and interactive video demos at our project page.

Reduced-order modeling (ROM) of time-dependent and parameterized differential equations aims to accelerate the simulation of complex high-dimensional systems by learning a compact latent manifold representation that captures the characteristics of the solution fields and their time-dependent dynamics. Although high-fidelity numerical solvers generate the training datasets, they have thus far been excluded from the training process, causing the learned latent dynamics to drift away from the discretized governing physics. This mismatch often limits generalization and forecasting capabilities. In this work, we propose Physics-informed ROM (Φ-ROM) by incorporating differentiable PDE solvers into the training procedure. Specifically, the latent space dynamics and its dependence on PDE parameters are shaped directly by the governing physics encoded in the solver, ensuring a strong correspondence between the full and reduced systems. Our model outperforms state-of-the-art data-driven ROMs and other physics-informed strategies by accurately generalizing to new dynamics arising from unseen parameters, enabling long-term forecasting beyond the training horizon, maintaining continuity in both time and space, and reducing the data cost. Furthermore, Φ-ROM learns to recover and forecast the solution fields even when trained or evaluated with sparse and irregular observations of the fields, providing a flexible framework for field reconstruction and data assimilation. We demonstrate the framework's robustness across various PDE solvers and highlight its broad applicability by providing an open-source JAX implementation that is readily extensible to other PDE systems and differentiable solvers, available at https://phi-rom.github.io.

Humanoid robots are promising to acquire various skills by imitating human behaviors. However, existing algorithms are only capable of tracking smooth, low-speed human motions, even with delicate reward and curriculum design. This paper presents a physics-based humanoid control framework, aiming to master highly-dynamic human behaviors such as Kungfu and dancing through multi-steps motion processing and adaptive motion tracking. For motion processing, we design a pipeline to extract, filter out, correct, and retarget motions, while ensuring compliance with physical constraints to the maximum extent. For motion imitation, we formulate a bi-level optimization problem to dynamically adjust the tracking accuracy tolerance based on the current tracking error, creating an adaptive curriculum mechanism. We further construct an asymmetric actor-critic framework for policy training. In experiments, we train whole-body control policies to imitate a set of highly-dynamic motions. Our method achieves significantly lower tracking errors than existing approaches and is successfully deployed on the Unitree G1 robot, demonstrating stable and expressive behaviors. The project page is https://kungfu-bot.github.io.

Action-conditioned world models (ACWMs) have shown strong promise for video prediction and decision-making. However, existing benchmarks are largely restricted to egocentric navigation or narrow, task-specific robotics datasets, offering only limited coverage of the rich physical interactions required for generalized world understanding. We introduce ACWM-Phys, a new benchmark for evaluating action-conditioned prediction under diverse physical dynamics in a clean, controllable simulation environment with a carefully designed action space. ACWM-Phys contains training and evaluation data spanning rigid-body dynamics, kinematics, deformable-object interactions, and particle dynamics. To evaluate both interpolation and generalization, we design in-distribution and out-of-distribution protocols with controlled shifts in interaction patterns or scene configurations. By building the benchmark in a fully controllable simulator, ACWM-Phys enables precise data collection, reproducible evaluation, and systematic analysis of model capabilities for physically grounded world modeling. Through systematic experiments on ACWM-DiT, we find that OoD generalization depends not only on the physical regime but also on effective task complexity: models generalize well on visually simple, low-dimensional interactions with clear geometric structure, but suffer larger drops on deformable contacts, high-dimensional control, and complex articulated motion. This suggests that the model still relies heavily on visual appearance patterns instead of fully learning the underlying physics. Ablations show that cross-attention improves high-dimensional action conditioning, causal VAEs outperform frame-wise encoders, and larger action spaces are harder to model but can improve generalization by providing richer control signals. These findings guide the design of physically grounded world models.

Accurate and efficient simulation of modern robots remains challenging due to their high degrees of freedom and intricate mechanisms. Neural simulators have emerged as a promising alternative to traditional analytical simulators, capable of efficiently predicting complex dynamics and adapting to real-world data; however, existing neural simulators typically require application-specific training and fail to generalize to novel tasks and/or environments, primarily due to inadequate representations of the global state. In this work, we address the problem of learning generalizable neural simulators for robots that are structured as articulated rigid bodies. We propose NeRD (Neural Robot Dynamics), learned robot-specific dynamics models for predicting future states for articulated rigid bodies under contact constraints. NeRD uniquely replaces the low-level dynamics and contact solvers in an analytical simulator and employs a robot-centric and spatially-invariant simulation state representation. We integrate the learned NeRD models as an interchangeable backend solver within a state-of-the-art robotics simulator. We conduct extensive experiments to show that the NeRD simulators are stable and accurate over a thousand simulation steps; generalize across tasks and environment configurations; enable policy learning exclusively in a neural engine; and, unlike most classical simulators, can be fine-tuned from real-world data to bridge the gap between simulation and reality.

Physical simulators have been widely used in robot planning and control. Among them, differentiable simulators are particularly favored, as they can be incorporated into gradient-based optimization algorithms that are efficient in solving inverse problems such as optimal control and motion planning. Simulating deformable objects is, however, more challenging compared to rigid body dynamics. The underlying physical laws of deformable objects are more complex, and the resulting systems have orders of magnitude more degrees of freedom and therefore they are significantly more computationally expensive to simulate. Computing gradients with respect to physical design or controller parameters is typically even more computationally challenging. In this paper, we propose a real-time, differentiable hybrid Lagrangian-Eulerian physical simulator for deformable objects, ChainQueen, based on the Moving Least Squares Material Point Method (MLS-MPM). MLS-MPM can simulate deformable objects including contact and can be seamlessly incorporated into inference, control and co-design systems. We demonstrate that our simulator achieves high precision in both forward simulation and backward gradient computation. We have successfully employed it in a diverse set of control tasks for soft robots, including problems with nearly 3,000 decision variables.

This document is a hands-on, comprehensive guide to deep learning in the realm of physical simulations. Rather than just theory, we emphasize practical application: every concept is paired with interactive Jupyter notebooks to get you up and running quickly. Beyond traditional supervised learning, we dive into physical loss-constraints, differentiable simulations, diffusion-based approaches for probabilistic generative AI, as well as reinforcement learning and advanced neural network architectures. These foundations are paving the way for the next generation of scientific foundation models. We are living in an era of rapid transformation. These methods have the potential to redefine what's possible in computational science.

The steep computational cost of diffusion models at inference hinders their use as fast physics emulators. In the context of image and video generation, this computational drawback has been addressed by generating in the latent space of an autoencoder instead of the pixel space. In this work, we investigate whether a similar strategy can be effectively applied to the emulation of dynamical systems and at what cost. We find that the accuracy of latent-space emulation is surprisingly robust to a wide range of compression rates (up to 1000x). We also show that diffusion-based emulators are consistently more accurate than non-generative counterparts and compensate for uncertainty in their predictions with greater diversity. Finally, we cover practical design choices, spanning from architectures to optimizers, that we found critical to train latent-space emulators.

In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology, geophysics, astrophysics and fluid dynamics. In the PINN framework, the governing partial differential equations, along with initial and boundary conditions, are encoded directly into the loss function, enabling the network to learn solutions that are consistent with the underlying physics. In this work, we employ the PINN framework to solve the dimensionless Navier-Stokes equations for three two-dimensional incompressible, steady, laminar flow problems without using any labeled data. The boundary and initial conditions are enforced in a hard manner, ensuring they are satisfied exactly rather than penalized during training. We validate the PINN predicted velocity profiles, drag coefficients and pressure profiles against the conventional computational fluid dynamics (CFD) simulations for moderate to high values of Reynolds number (Re). It is observed that the PINN predictions show good agreement with the CFD results at lower Re. We also extend our analysis to a transient condition and find that our method is equally capable of simulating complex time-dependent flow dynamics. To quantitatively assess the accuracy, we compute the L_2 normalized error, which lies in the range O(10^{-4}) - O(10^{-1}) for our chosen case studies.

Denoising diffusion models hold great promise for generating diverse and realistic human motions. However, existing motion diffusion models largely disregard the laws of physics in the diffusion process and often generate physically-implausible motions with pronounced artifacts such as floating, foot sliding, and ground penetration. This seriously impacts the quality of generated motions and limits their real-world application. To address this issue, we present a novel physics-guided motion diffusion model (PhysDiff), which incorporates physical constraints into the diffusion process. Specifically, we propose a physics-based motion projection module that uses motion imitation in a physics simulator to project the denoised motion of a diffusion step to a physically-plausible motion. The projected motion is further used in the next diffusion step to guide the denoising diffusion process. Intuitively, the use of physics in our model iteratively pulls the motion toward a physically-plausible space, which cannot be achieved by simple post-processing. Experiments on large-scale human motion datasets show that our approach achieves state-of-the-art motion quality and improves physical plausibility drastically (>78% for all datasets).

Large-scale video generative models, capable of creating realistic videos of diverse visual concepts, are strong candidates for general-purpose physical world simulators. However, their adherence to physical commonsense across real-world actions remains unclear (e.g., playing tennis, backflip). Existing benchmarks suffer from limitations such as limited size, lack of human evaluation, sim-to-real gaps, and absence of fine-grained physical rule analysis. To address this, we introduce VideoPhy-2, an action-centric dataset for evaluating physical commonsense in generated videos. We curate 200 diverse actions and detailed prompts for video synthesis from modern generative models. We perform human evaluation that assesses semantic adherence, physical commonsense, and grounding of physical rules in the generated videos. Our findings reveal major shortcomings, with even the best model achieving only 22% joint performance (i.e., high semantic and physical commonsense adherence) on the hard subset of VideoPhy-2. We find that the models particularly struggle with conservation laws like mass and momentum. Finally, we also train VideoPhy-AutoEval, an automatic evaluator for fast, reliable assessment on our dataset. Overall, VideoPhy-2 serves as a rigorous benchmark, exposing critical gaps in video generative models and guiding future research in physically-grounded video generation. The data and code is available at https://videophy2.github.io/.

Existing generative models for 3D shapes can synthesize high-fidelity and visually plausible shapes. For certain classes of shapes that have undergone an engineering design process, the realism of the shape is tightly coupled with the underlying physical properties, e.g., aerodynamic efficiency for automobiles. Since existing methods lack knowledge of such physics, they are unable to use this knowledge to enhance the realism of shape generation. Motivated by this, we propose a unified physics-based 3D shape generation pipeline, with a focus on industrial design applications. Specifically, we introduce a new flow matching model with explicit physical guidance, consisting of an alternating update process. We iteratively perform a velocity-based update and a physics-based refinement, progressively adjusting the latent code to align with the desired 3D shapes and physical properties. We further strengthen physical validity by incorporating a physics-aware regularization term into the velocity-based update step. To support such physics-guided updates, we build a shape-and-physics variational autoencoder (SP-VAE) that jointly encodes shape and physics information into a unified latent space. The experiments on three benchmarks show that this synergistic formulation improves shape realism beyond mere visual plausibility.

Reconstructing interactive, simulation-ready 3D scenes from a single image is a critical bottleneck for robotic manipulation. While recent single-image lifters recover plausible per-object shapes, composing them yields scenes that collapse under physical simulation due to interpenetrating, hovering, or sinking objects. Existing physics-aware methods address this strictly as a post-hoc layout correction, leaving the underlying geometric errors unresolved. To address this, we introduce SimuScene, a compositional 3D reconstruction pipeline that puts physics in the loop of shape and layout estimation. Rather than using physics merely for layout cleanup, we utilize the physics engine as a diagnostic measurement tool during the generative process itself. By diagnostically simulating reconstructed objects under gravity, we convert penetration and support failures into quantitative correction signals that drive gravity-axis stretching and amodal shape resampling. This physics-informed feedback loop mitigates accumulated reconstruction errors and produces a stable, simulation-ready compositional 3D scene. Extensive experiments demonstrate state-of-the-art performance on physical stability and geometric alignment benchmarks. We further highlight SimuScene's utility by deploying reconstructed environments in humanoid control and robot-arm manipulation tasks.

Deep learning models are increasingly employed for perception, prediction, and control in complex systems. Embedding physical knowledge into these models is crucial for achieving realistic and consistent outputs, a challenge often addressed by physics-informed machine learning. However, integrating physical knowledge with representation learning becomes difficult when dealing with high-dimensional observation data, such as images, particularly under conditions of incomplete or imprecise state information. To address this, we propose Physically Interpretable World Models, a novel architecture that aligns learned latent representations with real-world physical quantities. Our method combines a variational autoencoder with a dynamical model that incorporates unknown system parameters, enabling the discovery of physically meaningful representations. By employing weak supervision with interval-based constraints, our approach eliminates the reliance on ground-truth physical annotations. Experimental results demonstrate that our method improves the quality of learned representations while achieving accurate predictions of future states, advancing the field of representation learning in dynamic systems.

Unknown dynamic load carrying is one important practical application for quadruped robots. Such a problem is non-trivial, posing three major challenges in quadruped locomotion control. First, how to model or represent the dynamics of the load in a generic manner. Second, how to make the robot capture the dynamics without any external sensing. Third, how to enable the robot to interact with load handling the mutual effect and stabilizing the load. In this work, we propose a general load modeling approach called load characteristics modeling to capture the dynamics of the load. We integrate this proposed modeling technique and leverage recent advances in Reinforcement Learning (RL) based locomotion control to enable the robot to infer the dynamics of load movement and interact with the load indirectly to stabilize it and realize the sim-to-real deployment to verify its effectiveness in real scenarios. We conduct extensive comparative simulation experiments to validate the effectiveness and superiority of our proposed method. Results show that our method outperforms other methods in sudden load resistance, load stabilizing and locomotion with heavy load on rough terrain. https://leixinjonaschang.github.io/leggedloadadapt.github.io/{Project Page}.

Achieving both realism and controllability in interactive closed-loop traffic simulation remains a key challenge in autonomous driving. Data-driven simulation methods reproduce realistic trajectories but suffer from covariate shift in closed-loop deployment, compounded by simplified dynamics models that further reduce reliability. Conversely, physics-based simulation methods enhance reliable and controllable closed-loop interactions but often lack expert demonstrations, compromising realism. To address these challenges, we introduce a dual-stage AV-centered simulation framework that conducts open-loop imitation learning pre-training in a data-driven simulator to capture trajectory-level realism and multimodality, followed by closed-loop reinforcement learning fine-tuning in a physics-based simulator to enhance controllability and mitigate covariate shift. In the fine-tuning stage, we propose RIFT, a simple yet effective closed-loop RL fine-tuning strategy that preserves the trajectory-level multimodality through a GRPO-style group-relative advantage formulation, while enhancing controllability and training stability by replacing KL regularization with the dual-clip mechanism. Extensive experiments demonstrate that RIFT significantly improves the realism and controllability of generated traffic scenarios, providing a robust platform for evaluating autonomous vehicle performance in diverse and interactive scenarios.

Accurately simulating real world object dynamics is essential for various applications such as robotics, engineering, graphics, and design. To better capture complex real dynamics such as contact and friction, learned simulators based on graph networks have recently shown great promise. However, applying these learned simulators to real scenes comes with two major challenges: first, scaling learned simulators to handle the complexity of real world scenes which can involve hundreds of objects each with complicated 3D shapes, and second, handling inputs from perception rather than 3D state information. Here we introduce a method which substantially reduces the memory required to run graph-based learned simulators. Based on this memory-efficient simulation model, we then present a perceptual interface in the form of editable NeRFs which can convert real-world scenes into a structured representation that can be processed by graph network simulator. We show that our method uses substantially less memory than previous graph-based simulators while retaining their accuracy, and that the simulators learned in synthetic environments can be applied to real world scenes captured from multiple camera angles. This paves the way for expanding the application of learned simulators to settings where only perceptual information is available at inference time.

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in phase space dynamics, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each presents its unique limitations and generally balances training cost, numerical accuracy, and ease of applicability to different problem setups. To address these limitations, we introduce several methods to apply latent diffusion models to physics simulation. Firstly, we introduce a mesh autoencoder to compress arbitrarily discretized PDE data, allowing for efficient diffusion training across various physics. Furthermore, we investigate full spatio-temporal solution generation to mitigate autoregressive error accumulation. Lastly, we investigate conditioning on initial physical quantities, as well as conditioning solely on a text prompt to introduce text2PDE generation. We show that language can be a compact, interpretable, and accurate modality for generating physics simulations, paving the way for more usable and accessible PDE solvers. Through experiments on both uniform and structured grids, we show that the proposed approach is competitive with current neural PDE solvers in both accuracy and efficiency, with promising scaling behavior up to sim3 billion parameters. By introducing a scalable, accurate, and usable physics simulator, we hope to bring neural PDE solvers closer to practical use.

We present Dojo, a differentiable physics engine for robotics that prioritizes stable simulation, accurate contact physics, and differentiability with respect to states, actions, and system parameters. Dojo models hard contact and friction with a nonlinear complementarity problem with second-order cone constraints. We introduce a custom primal-dual interior-point method to solve the second order cone program for stable forward simulation over a broad range of sample rates. We obtain smooth gradient approximations with this solver through the implicit function theorem, giving gradients that are useful for downstream trajectory optimization, policy optimization, and system identification applications. Specifically, we propose to use the central path parameter threshold in the interior point solver as a user-tunable design parameter. A high value gives a smooth approximation to contact dynamics with smooth gradients for optimization and learning, while a low value gives precise simulation rollouts with hard contact. We demonstrate Dojo's differentiability in trajectory optimization, policy learning, and system identification examples. We also benchmark Dojo against MuJoCo, PyBullet, Drake, and Brax on a variety of robot models, and study the stability and simulation quality over a range of sample frequencies and accuracy tolerances. Finally, we evaluate the sim-to-real gap in hardware experiments with a Ufactory xArm 6 robot. Dojo is an open source project implemented in Julia with Python bindings, with code available at https://github.com/dojo-sim/Dojo.jl.

Training sophisticated machine learning (ML) models requires large datasets that are difficult or expensive to collect for many applications. If prior knowledge about system dynamics is available, mechanistic representations can be used to supplement real-world data. We present SimbaML (Simulation-Based ML), an open-source tool that unifies realistic synthetic dataset generation from ordinary differential equation-based models and the direct analysis and inclusion in ML pipelines. SimbaML conveniently enables investigating transfer learning from synthetic to real-world data, data augmentation, identifying needs for data collection, and benchmarking physics-informed ML approaches. SimbaML is available from https://pypi.org/project/simba-ml/.

Learning complex dynamics driven by partial differential equations directly from data holds great promise for fast and accurate simulations of complex physical systems. In most cases, this problem can be formulated as an operator learning task, where one aims to learn the operator representing the physics of interest, which entails discretization of the continuous system. However, preserving key continuous properties at the discrete level, such as boundary conditions, and addressing physical systems with complex geometries is challenging for most existing approaches. We introduce a family of operator learning architectures, structure-preserving operator networks (SPONs), that allows to preserve key mathematical and physical properties of the continuous system by leveraging finite element (FE) discretizations of the input-output spaces. SPONs are encode-process-decode architectures that are end-to-end differentiable, where the encoder and decoder follows from the discretizations of the input-output spaces. SPONs can operate on complex geometries, enforce certain boundary conditions exactly, and offer theoretical guarantees. Our framework provides a flexible way of devising structure-preserving architectures tailored to specific applications, and offers an explicit trade-off between performance and efficiency, all thanks to the FE discretization of the input-output spaces. Additionally, we introduce a multigrid-inspired SPON architecture that yields improved performance at higher efficiency. Finally, we release a software to automate the design and training of SPON architectures.

We propose a hybrid neural network (NN) and PDE approach for learning generalizable PDE dynamics from motion observations. Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and constitutive models (or material models). Without explicit PDE knowledge, these approaches cannot guarantee physical correctness and have limited generalizability. We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned. Instead, constitutive models are particularly suitable for learning due to their data-fitting nature. To this end, we introduce a new framework termed "Neural Constitutive Laws" (NCLaw), which utilizes a network architecture that strictly guarantees standard constitutive priors, including rotation equivariance and undeformed state equilibrium. We embed this network inside a differentiable simulation and train the model by minimizing a loss function based on the difference between the simulation and the motion observation. We validate NCLaw on various large-deformation dynamical systems, ranging from solids to fluids. After training on a single motion trajectory, our method generalizes to new geometries, initial/boundary conditions, temporal ranges, and even multi-physics systems. On these extremely out-of-distribution generalization tasks, NCLaw is orders-of-magnitude more accurate than previous NN approaches. Real-world experiments demonstrate our method's ability to learn constitutive laws from videos.

Video generative models pre-trained on large-scale internet datasets have achieved remarkable success, excelling at producing realistic synthetic videos. However, they often generate clips based on static prompts (e.g., text or images), limiting their ability to model interactive and dynamic scenarios. In this paper, we propose Dynamic World Simulation (DWS), a novel approach to transform pre-trained video generative models into controllable world simulators capable of executing specified action trajectories. To achieve precise alignment between conditioned actions and generated visual changes, we introduce a lightweight, universal action-conditioned module that seamlessly integrates into any existing model. Instead of focusing on complex visual details, we demonstrate that consistent dynamic transition modeling is the key to building powerful world simulators. Building upon this insight, we further introduce a motion-reinforced loss that enhances action controllability by compelling the model to capture dynamic changes more effectively. Experiments demonstrate that DWS can be versatilely applied to both diffusion and autoregressive transformer models, achieving significant improvements in generating action-controllable, dynamically consistent videos across games and robotics domains. Moreover, to facilitate the applications of the learned world simulator in downstream tasks such as model-based reinforcement learning, we propose prioritized imagination to improve sample efficiency, demonstrating competitive performance compared with state-of-the-art methods.

Despite recent progress, video diffusion models still struggle to synthesize realistic videos involving highly dynamic motions or requiring fine-grained motion controllability. A central limitation lies in the scarcity of such examples in commonly used training datasets. To address this, we introduce DynaVid, a video synthesis framework that leverages synthetic motion data in training, which is represented as optical flow and rendered using computer graphics pipelines. This approach offers two key advantages. First, synthetic motion offers diverse motion patterns and precise control signals that are difficult to obtain from real data. Second, unlike rendered videos with artificial appearances, rendered optical flow encodes only motion and is decoupled from appearance, thereby preventing models from reproducing the unnatural look of synthetic videos. Building on this idea, DynaVid adopts a two-stage generation framework: a motion generator first synthesizes motion, and then a motion-guided video generator produces video frames conditioned on that motion. This decoupled formulation enables the model to learn dynamic motion patterns from synthetic data while preserving visual realism from real-world videos. We validate our framework on two challenging scenarios, vigorous human motion generation and extreme camera motion control, where existing datasets are particularly limited. Extensive experiments demonstrate that DynaVid improves the realism and controllability in dynamic motion generation and camera motion control.

The scarcity of large-scale robotic data has motivated the repurposing of foundation models from other modalities for policy learning. In this work, we introduce PhysGen (Learning Physics from Pretrained Video Generation Models), a scalable continuous and sequential world interaction framework that leverages autoregressive video generation to solve robotic manipulation tasks. By treating the pretrained video model as a proxy for a physics simulator, PhysGen models the dynamic interplay between the external environment and robot actions. We introduce a multimodal continuous representation that unifies video and action into shared physical tokens, bridging the gap between discrete video generation and continuous robotic control. This approach enables the seamless transfer of implicit physical knowledge-such as object permanence and dynamics-from video pretraining to downstream manipulation.To ensure efficient convergence, we incorporate causal masking, inverse kinematics, Lookahead Multi-Token Prediction (L-MTP), and key-value (KV) caching. Experimental results on the Libero and ManiSkill benchmarks demonstrate that PhysGen consistently outperforms robust baselines, surpassing OpenVLA and WorldVLA by margins of 13.8% and 8.8%, respectively. Notably, in real-world scenarios, PhysGen matches the performance of large-scale action-pretrained models like π_0 without requiring prior action-specific pretraining, demonstrating superior capability in physically complex tasks such as grasping transparent objects. These findings validate the potential of extracting physical intuition from pretrained video generators to facilitate generalizable robotic manipulation.

Model-free control strategies such as reinforcement learning have shown the ability to learn control strategies without requiring an accurate model or simulator of the world. While this is appealing due to the lack of modeling requirements, such methods can be sample inefficient, making them impractical in many real-world domains. On the other hand, model-based control techniques leveraging accurate simulators can circumvent these challenges and use a large amount of cheap simulation data to learn controllers that can effectively transfer to the real world. The challenge with such model-based techniques is the requirement for an extremely accurate simulation, requiring both the specification of appropriate simulation assets and physical parameters. This requires considerable human effort to design for every environment being considered. In this work, we propose a learning system that can leverage a small amount of real-world data to autonomously refine a simulation model and then plan an accurate control strategy that can be deployed in the real world. Our approach critically relies on utilizing an initial (possibly inaccurate) simulator to design effective exploration policies that, when deployed in the real world, collect high-quality data. We demonstrate the efficacy of this paradigm in identifying articulation, mass, and other physical parameters in several challenging robotic manipulation tasks, and illustrate that only a small amount of real-world data can allow for effective sim-to-real transfer. Project website at https://weirdlabuw.github.io/asid

Current video generation models cannot simulate physical consequences of 3D actions like forces and robotic manipulations, as they lack structural understanding of how actions affect 3D scenes. We present RealWonder, the first real-time system for action-conditioned video generation from a single image. Our key insight is using physics simulation as an intermediate bridge: instead of directly encoding continuous actions, we translate them through physics simulation into visual representations (optical flow and RGB) that video models can process. RealWonder integrates three components: 3D reconstruction from single images, physics simulation, and a distilled video generator requiring only 4 diffusion steps. Our system achieves 13.2 FPS at 480x832 resolution, enabling interactive exploration of forces, robot actions, and camera controls on rigid objects, deformable bodies, fluids, and granular materials. We envision RealWonder opens new opportunities to apply video models in immersive experiences, AR/VR, and robot learning. Our code and model weights are publicly available in our project website: https://liuwei283.github.io/RealWonder/

Generative video models achieve high visual fidelity but often violate basic physical principles, limiting reliability in real-world settings. Prior attempts to inject physics rely on conditioning: frame-level signals are domain-specific and short-horizon, while global text prompts are coarse and noisy, missing fine-grained dynamics. We present PhysVid, a physics-aware local conditioning scheme that operates over temporally contiguous chunks of frames. Each chunk is annotated with physics-grounded descriptions of states, interactions, and constraints, which are fused with the global prompt via chunk-aware cross-attention during training. At inference, we introduce negative physics prompts (descriptions of locally relevant law violations) to steer generation away from implausible trajectories. On VideoPhy, PhysVid improves physical commonsense scores by approx 33% over baseline video generators, and by up to approx 8% on VideoPhy2. These results show that local, physics-aware guidance substantially increases physical plausibility in generative video and marks a step toward physics-grounded video models.

Video generation models are increasingly used as world simulators for storytelling, simulation, and embodied AI. As these models advance, a key question arises: do generated videos obey the physical laws of the real world? Existing evaluations largely rely on automated metrics or coarse human judgments such as preferences or rubric-based checks. While useful for assessing perceptual quality, these methods provide limited insight into when and why generated dynamics violate real-world physical constraints. We introduce Physion-Eval, a large-scale benchmark of expert human reasoning for diagnosing physical realism failures in videos generated by five state-of-the-art models across egocentric and exocentric views, containing 10,990 expert reasoning traces spanning 22 fine-grained physical categories. Each generated video is derived from a corresponding real-world reference video depicting a clear physical process, and annotated with temporally localized glitches, structured failure categories, and natural-language explanations of the violated physical behavior. Using this dataset, we reveal a striking limitation of current video generation models: in physics-critical scenarios, 83.3% of exocentric and 93.5% of egocentric generated videos exhibit at least one human-identifiable physical glitch. We hope Physion-Eval will set a new standard for physical realism evaluation and guide the development of physics-grounded video generation. The benchmark is publicly available at https://huggingface.co/datasets/PhysionLabs/Physion-Eval.

Navigation and manipulation are core capabilities in Embodied AI, yet training agents with these capabilities in the real world faces high costs and time complexity. Therefore, sim-to-real transfer has emerged as a key approach, yet the sim-to-real gap persists. This survey examines how physics simulators address this gap by analyzing their properties overlooked in previous surveys. We also analyze their features for navigation and manipulation tasks, along with hardware requirements. Additionally, we offer a resource with benchmark datasets, metrics, simulation platforms, and cutting-edge methods-such as world models and geometric equivariance-to help researchers select suitable tools while accounting for hardware constraints.

While non-prehensile manipulation (e.g., controlled pushing/poking) constitutes a foundational robotic skill, its learning remains challenging due to the high sensitivity to complex physical interactions involving friction and restitution. To achieve robust policy learning and generalization, we opt to learn a world model of the 3D rigid body dynamics involved in non-prehensile manipulations and use it for model-based reinforcement learning. We propose PIN-WM, a Physics-INformed World Model that enables efficient end-to-end identification of a 3D rigid body dynamical system from visual observations. Adopting differentiable physics simulation, PIN-WM can be learned with only few-shot and task-agnostic physical interaction trajectories. Further, PIN-WM is learned with observational loss induced by Gaussian Splatting without needing state estimation. To bridge Sim2Real gaps, we turn the learned PIN-WM into a group of Digital Cousins via physics-aware randomizations which perturb physics and rendering parameters to generate diverse and meaningful variations of the PIN-WM. Extensive evaluations on both simulation and real-world tests demonstrate that PIN-WM, enhanced with physics-aware digital cousins, facilitates learning robust non-prehensile manipulation skills with Sim2Real transfer, surpassing the Real2Sim2Real state-of-the-arts.

Accurate and efficient physical simulations are essential in science and engineering, yet traditional numerical solvers face significant challenges in computational cost when handling simulations across dynamic scenarios involving complex geometries, varying boundary/initial conditions, and diverse physical parameters. While deep learning offers promising alternatives, existing methods often struggle with flexibility and generalization, particularly on unstructured meshes, which significantly limits their practical applicability. To address these challenges, we propose PhysGTO, an efficient Graph-Transformer Operator for learning physical dynamics through explicit manifold embeddings in both physical and latent spaces. In the physical space, the proposed Unified Graph Embedding module aligns node-level conditions and constructs sparse yet structure-preserving graph connectivity to process heterogeneous inputs. In the latent space, PhysGTO integrates a lightweight flux-oriented message-passing scheme with projection-inspired attention to capture local and global dependencies, facilitating multilevel interactions among complex physical correlations. This design ensures linear complexity relative to the number of mesh points, reducing both the number of trainable parameters and computational costs in terms of floating-point operations (FLOPs), and thereby allowing efficient inference in real-time applications. We introduce a comprehensive benchmark spanning eleven datasets, covering problems with unstructured meshes, transient flow dynamics, and large-scale 3D geometries. PhysGTO consistently achieves state-of-the-art accuracy while significantly reducing computational costs, demonstrating superior flexibility, scalability, and generalization in a wide range of simulation tasks.

Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental challenge, as existing approaches face a critical speed-fidelity trade-off. In this work, we introduce Recursive Flow Matching (RecFM), a generative framework for forecasting complex spatiotemporal dynamics. RecFM enforces self-consistency to align trajectories across discretization scales, reducing discretization errors and improving performance across metrics for physics-based tasks. To our knowledge, this is the first method to achieve high-fidelity one- and few-step (2-4 step) dynamic generation for scientific systems with performance comparable to state-of-the-art multi-step solvers. Across challenging scientific benchmarks, RecFM achieves up to a 20times speedup over leading diffusion-based emulators while improving predictive accuracy. Furthermore, RecFM reduces mean squared error by over 15% compared to vanilla flow matching, offering a scalable and efficient solution for real-time scientific emulation.

It is desired to equip robots with the capability of interacting with various soft materials as they are ubiquitous in the real world. While physics simulations are one of the predominant methods for data collection and robot training, simulating soft materials presents considerable challenges. Specifically, it is significantly more costly than simulating rigid objects in terms of simulation speed and storage requirements. These limitations typically restrict the scope of studies on soft materials to small and bounded areas, thereby hindering the learning of skills in broader spaces. To address this issue, we introduce UBSoft, a new simulation platform designed to support unbounded soft environments for robot skill acquisition. Our platform utilizes spatially adaptive resolution scales, where simulation resolution dynamically adjusts based on proximity to active robotic agents. Our framework markedly reduces the demand for extensive storage space and computation costs required for large-scale scenarios involving soft materials. We also establish a set of benchmark tasks in our platform, including both locomotion and manipulation tasks, and conduct experiments to evaluate the efficacy of various reinforcement learning algorithms and trajectory optimization techniques, both gradient-based and sampling-based. Preliminary results indicate that sampling-based trajectory optimization generally achieves better results for obtaining one trajectory to solve the task. Additionally, we conduct experiments in real-world environments to demonstrate that advancements made in our UBSoft simulator could translate to improved robot interactions with large-scale soft material. More videos can be found at https://vis-www.cs.umass.edu/ubsoft/.

Implicit Neural Spatial Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR. Classical PDE solvers introduce both temporal and spatial discretizations. Common spatial discretizations include meshes and meshless point clouds, where each degree-of-freedom corresponds to a location in space. While these explicit spatial correspondences are intuitive to model and understand, these representations are not necessarily optimal for accuracy, memory usage, or adaptivity. Keeping the classical temporal discretization unchanged (e.g., explicit/implicit Euler), we explore INSR as an alternative spatial discretization, where spatial information is implicitly stored in the neural network weights. The network weights then evolve over time via time integration. Our approach does not require any training data generated by existing solvers because our approach is the solver itself. We validate our approach on various PDEs with examples involving large elastic deformations, turbulent fluids, and multi-scale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy and lower memory consumption. Whereas classical solvers can dynamically adapt their spatial representation only by resorting to complex remeshing algorithms, our INSR approach is intrinsically adaptive. By tapping into the rich literature of classic time integrators, e.g., operator-splitting schemes, our method enables challenging simulations in contact mechanics and turbulent flows where previous neural-physics approaches struggle. Videos and codes are available on the project page: http://www.cs.columbia.edu/cg/INSR-PDE/

We address the task of generating physically accurate and visually faithful 4D Human-Object Interaction (HOI). Given a static 3D human and target object represented as 3D Gaussian Splats (3DGS), our goal is to synthesize dynamic scenes where the human actively engages with the object through actions, such as punching or kicking, in accordance with a given input text. To this end, we introduce PhyGenHOI, a novel framework that couples generative human motion with an explicit physical object simulation. We model the human as a semantic agent driven by a Motion Diffusion Model (MDM) and the object as a physical agent simulated via the Material Point Method (MPM), utilizing 3D Gaussians as a unified, differentiable representation. We supervise their interaction through three coupled mechanisms: (1) A Windowed Attraction Loss that temporally synchronizes generative motion to intercept the object; (2) A Contact-Driven Re-simulation step that triggers physically consistent momentum transfer upon impact; and (3) A Masked Video-SDS objective that injects video-based priors to enhance contact fidelity. Experiments show PhyGenHOI generates physically consistent 4D HOI across diverse actions, humans, and objects, outperforming baselines. Project page and videos: https://omerbenishu.github.io/PhyGenHOI/

We consider the problem of forecasting motion from a single image, i.e., predicting how objects in the world are likely to move, without the ability to observe other parameters such as the object velocities or the forces applied to them. We formulate this task as conditional generation of dense trajectory grids with a model that closely follows the architecture of modern video generators but outputs motion trajectories instead of pixels. This approach captures scene-wide dynamics and uncertainty, yielding more accurate and diverse predictions than prior regressors and generators. We extensively evaluate our method on simulated data, demonstrate its effectiveness on downstream applications such as robotics, and show promising accuracy on real-world intuitive physics datasets. Although recent state-of-the-art video generators are often regarded as world models, we show that they struggle with forecasting motion from a single image, even in simple physical scenarios such as falling blocks or mechanical object interactions, despite fine-tuning on such data. We show that this limitation arises from the overhead of generating pixels rather than directly modeling motion.

Modeling and synthesizing complex hand-object interactions remains a significant challenge, even for state-of-the-art physics engines. Conventional simulation-based approaches rely on explicitly defined rigid object models and pre-scripted hand gestures, making them inadequate for capturing dynamic interactions with non-rigid or articulated entities such as deformable fabrics, elastic materials, hinge-based structures, furry surfaces, or even living creatures. In this paper, we present SpriteHand, an autoregressive video generation framework for real-time synthesis of versatile hand-object interaction videos across a wide range of object types and motion patterns. SpriteHand takes as input a static object image and a video stream in which the hands are imagined to interact with the virtual object embedded in a real-world scene, and generates corresponding hand-object interaction effects in real time. Our model employs a causal inference architecture for autoregressive generation and leverages a hybrid post-training approach to enhance visual realism and temporal coherence. Our 1.3B model supports real-time streaming generation at around 18 FPS and 640x368 resolution, with an approximate 150 ms latency on a single NVIDIA RTX 5090 GPU, and more than a minute of continuous output. Experiments demonstrate superior visual quality, physical plausibility, and interaction fidelity compared to both generative and engine-based baselines.

Recent models for video generation have achieved remarkable progress and are now deployed in film, social media production, and advertising. Beyond their creative potential, such models also hold promise as world simulators for robotics and embodied decision making. Despite strong advances, however, current approaches still struggle to generate physically plausible object interactions and lack physics-grounded control mechanisms. To address this limitation, we introduce KineMask, an approach for physics-guided video generation that enables realistic rigid body control, interactions, and effects. Given a single image and a specified object velocity, our method generates videos with inferred motions and future object interactions. We propose a two-stage training strategy that gradually removes future motion supervision via object masks. Using this strategy we train video diffusion models (VDMs) on synthetic scenes of simple interactions and demonstrate significant improvements of object interactions in real scenes. Furthermore, KineMask integrates low-level motion control with high-level textual conditioning via predictive scene descriptions, leading to effective support for synthesis of complex dynamical phenomena. Extensive experiments show that KineMask achieves strong improvements over recent models of comparable size. Ablation studies further highlight the complementary roles of low- and high-level conditioning in VDMs. Our code, model, and data will be made publicly available.

This study introduces amangkurat, an open-source Python library designed for the robust numerical simulation of relativistic scalar field dynamics governed by the nonlinear Klein-Gordon equation in (1+1)D spacetime. The software implements a hybrid computational strategy that couples Fourier pseudo-spectral spatial discretization with a symplectic Størmer-Verlet temporal integrator, ensuring both exponential spatial convergence for smooth solutions and long-term preservation of Hamiltonian structure. To optimize performance, the solver incorporates adaptive timestepping based on Courant-Friedrichs-Lewy (CFL) stability criteria and utilizes Just-In-Time (JIT) compilation for parallelized force computation. The library's capabilities are validated across four canonical physical regimes: dispersive linear wave propagation, static topological kink preservation in phi-fourth theory, integrable breather dynamics in the sine-Gordon model, and non-integrable kink-antikink collisions. Beyond standard numerical validation, this work establishes a multi-faceted analysis framework employing information-theoretic entropy metrics (Shannon, Rényi, and Tsallis), kernel density estimation, and phase space reconstruction to quantify the distinct phenomenological signatures of these regimes. Statistical hypothesis testing confirms that these scenarios represent statistically distinguishable dynamical populations. Benchmarks on standard workstation hardware demonstrate that the implementation achieves high computational efficiency, making it a viable platform for exploratory research and education in nonlinear field theory.

The intrinsic dynamics of an object governs its physical behavior in the real world, playing a critical role in enabling physically plausible interactive simulation with 3D assets. Existing methods have attempted to infer the intrinsic dynamics of objects from visual observations, but generally face two major challenges: one line of work relies on manually defined constitutive priors, making it difficult to generalize to complex scenarios; the other models intrinsic dynamics using neural networks, resulting in limited interpretability and poor generalization. To address these challenges, we propose VisionLaw, a bilevel optimization framework that infers interpretable expressions of intrinsic dynamics from visual observations. At the upper level, we introduce an LLMs-driven decoupled constitutive evolution strategy, where LLMs are prompted as a knowledgeable physics expert to generate and revise constitutive laws, with a built-in decoupling mechanism that substantially reduces the search complexity of LLMs. At the lower level, we introduce a vision-guided constitutive evaluation mechanism, which utilizes visual simulation to evaluate the consistency between the generated constitutive law and the underlying intrinsic dynamics, thereby guiding the upper-level evolution. Experiments on both synthetic and real-world datasets demonstrate that VisionLaw can effectively infer interpretable intrinsic dynamics from visual observations. It significantly outperforms existing state-of-the-art methods and exhibits strong generalization for interactive simulation in novel scenarios.