PowerSim: Differentiable Physics Simulation and Rendering with Power Diagrams

To study the ability to infer physical dynamics from videos and extrapolate them forward in time, we assemble a dataset of 2D Material Point Method (MPM) physical simulations covering rich physical phenomena such as deformable objects, fluids, kinetic objects, and emitters. We study code generation and video diffusion approaches on this dataset, identifying their strengths and weaknesses by varying the amount of physically relevant side information. The code generation model, beyond giving a working demonstration of automatic synthesis of MPM simulations, reveals that such an approach struggles with inferring physical parameters from visual input, but relative to video diffusion, produces physically and temporally stable extrapolations forward in time, while the video diffusion model more strongly identifies geometric properties from visual input but produces physically implausible extrapolations.

We introduce a differentiable 3D representation that unifies the ray tracing capabilities of foam-based ray tracing with the efficiency of modern rasterization pipelines. While prior foam representations enable constant-time ray traversal through an explicit volumetric partition of space, their potentially unbounded cells hinder efficient tile-based rasterization. We address this limitation by generalizing Voronoi foams to bounded power diagrams with controllable cell extents, enabling spatially bounded primitives without requiring expensive Delaunay triangulations during training. We further introduce an oriented surface formulation that explicitly models interfaces between interior and exterior regions, and decouple geometry from appearance by embedding differentiable texture directly on these surfaces. Together, these contributions yield a representation that preserves state-of-the-art ray tracing efficiency while achieving rasterization performance competitive with current generation 3DGS, providing a practical path toward unified real-time differentiable rendering.

Learning physically plausible dynamics from visual observations is essential for interactive world models and embodied agents. However, modeling real-world deformable objects remains challenging because their dynamics often arise from complex, spatially heterogeneous material responses. To address this challenge, we propose PhysReal, a video-driven framework for learning and simulating the underlying physics of real deformable objects. PhysReal integrates a spatially varying hybrid expert-neural constitutive model with a differentiable MPM simulator and 3DGS renderer. Analytical expert models provide interpretable physical priors, while neural constitutive residuals capture material responses beyond predefined formulations. Spatially distributed patches parameterize the constitutive field, enabling a continuous representation of local material variations. To organize the identification of this model from sparse visual observations, we adopt a progressive curriculum that sequentially optimizes global material properties, spatially varying local parameters, and neural constitutive residuals, together with complementary motion and mask supervision. Extensive experiments on diverse deformable-object interactions demonstrate that PhysReal achieves superior performance in dynamic reconstruction and future-state prediction, while showing strong potential for downstream robotic applications.