Integrating Physics and Topology in Neural Networks for Learning Rigid Body Dynamics

Amaury Wei, Olga Fink
IMOS laboratory
Ecole Polytechnique Federale de Lausanne (EPFL)
Nature Communications (2025)
Paper Supplementary Code Data arXiv
HOPNet method overview

Overview of HOPNet. (a) Autoregressive rollout approach; (b) Physics-informed message-passing strategy. Our sequential message-passing is inspired by Newtonian laws and tailored to process collisions. It first processes ongoing collisions (steps 1, 2, and 3) and then updates individual objects (steps 4 and 5). Finally, the per-node and per-object accelerations are computed (step 6) and the final object poses are obtained (step 7) with shape matching.

Abstract

Rigid body interactions are fundamental to numerous scientific disciplines, but remain challenging to simulate due to their abrupt nonlinear nature and sensitivity to complex, often unknown environmental factors. These challenges call for adaptable learning-based methods capable of capturing complex interactions beyond explicit physical models and simulations. While graph neural networks can handle simple scenarios, they struggle with complex scenes and long-term predictions. We introduce a novel framework for modeling rigid body dynamics and learning collision interactions, addressing key limitations of existing graph-based methods. Our approach extends the traditional representation of meshes by incorporating higher-order topology complexes, offering a physically consistent representation. Additionally, we propose a physics-informed message-passing neural architecture, embedding physical laws directly in the model. Our method demonstrates superior accuracy, even during long rollouts, and exhibits strong generalization to unseen scenarios. Importantly, this work addresses the challenge of multi-entity dynamic interactions, with applications spanning diverse scientific and engineering domains.

Rigid Body Scenes as Combinatorial Complexes

Traditional graph-based simulators represent rigid-body scenes using basic node and edge connections, which often overlook the structure of mesh surfaces and the integrity of individual objects. Our method introduces a more expressive representation by modeling the environment as a Combinatorial Complex—a hierarchical structure that explicitly encodes nodes, mesh triangles, object identities, and collisions. This higher-order approach preserves both geometry and physics, enabling more accurate modeling of rigid-body interactions. By processing sequences of these structures over time, our model can predict future object states through autoregressive rollouts.

Rigid body scenes as combinatorial complexes

Spatiotemporal combinatorial complexes. (a) Real-world observations are represented by (b) spatiotemporal combinatorial complexes. The topology and features of each combinatorial complex evolve over time to accurately represent the environment.

Physics-informed Message-passing

HOPNet introduces a physics-informed message-passing framework that mirrors how forces and collisions propagate in the real world. Instead of relying on generic node-to-node communication, our model exchanges learnable messages along structured pathways defined by Newtonian principles, using a higher-order representation of the scene. This approach improves accuracy, efficiency, and interpretability by explicitly modeling energy and momentum transfer during collisions. Combined with a second-order integrator and shape-matching for object-level updates, HOPNet produces stable and realistic rollouts of complex rigid body interactions.

Physics-informed message-passing

Physics-informed message-passing. (a) Enhancing mesh face cells embeddings with nodes, edges, and object cells;
(b) Computing the effect of a collision from two mesh faces s and r on each other; (c) Updating triangles s and r after collisions.

Results

We evaluate HOPNet on four progressively complex datasets (MOVi-spheres, MOVi-A, MOVi-B, MOVi-C) involving realistic 3D object collisions, demonstrating superior accuracy over existing graph-based simulators. Our model produces stable long-term rollouts and maintains low error over time, outperforming prior methods like FIGNet and MeshGraphNet by a large margin. HOPNet also generalizes well to unseen object geometries—even when trained only on simple shapes—thanks to its physics-informed architecture and topological representation. Additional experiments show that exposure to diverse, dynamic collisions during training significantly improves generalization, highlighting the model’s robustness.

Rollout Videos

We show multiple autoregressive rollout videos showing HOPNet's predictions over 240 rollout timesteps alongside ground-truth trajectories across several trajectories. The videos are played back at 50% speed to improve visibility of the dynamics.

Counterfactual Reasoning

HOPNet supports robust counterfactual reasoning by accurately simulating how a scene evolves under hypothetical changes—such as altering object positions, velocities, or removing elements entirely. Unlike traditional models that struggle with long-term predictions under novel conditions, HOPNet maintains high accuracy even in out-of-distribution scenarios and exceeds prior methods by over 50% in rollout duration at comparable error levels. This makes it especially well-suited for applications in planning, analysis, and decision-making. Below, we provide an interactive demo where you can remove an object from a scene and view HOPNet’s predicted outcomes in response.


MOVi-A sample 6

BibTeX

@Article{Wei2025,
  author={Wei, Amaury and Fink, Olga},
  title={Integrating physics and topology in neural networks for learning rigid body dynamics},
  journal={Nature Communications},
  year={2025},
  month={Jul},
  day={25},
  volume={16},
  number={1},
  pages={6867},
  issn={2041-1723},
  doi={10.1038/s41467-025-62250-7},
  url={https://doi.org/10.1038/s41467-025-62250-7}
}