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

arXiv: https://arxiv.org/abs/2411.11467 · HTML: https://mlsanity.com/paper/2411.11467/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 53 references that are in the map.
- First posted on arXiv 18 Nov 2024.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Google Scanned Objects: A High-Quality Dataset of 3D Scanned Household Items](https://mlsanity.com/paper/2204.11918/) (2022)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [Kubric: A scalable dataset generator](https://mlsanity.com/paper/2203.03570/) (2022)
- [Conditional Object-Centric Learning from Video](https://mlsanity.com/paper/2111.12594/) (2021)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [Weisfeiler and Lehman Go Cellular: CW Networks](https://mlsanity.com/paper/2106.12575/) (2021)
- [ChemRL-GEM: Geometry Enhanced Molecular Representation Learning for Property Prediction](https://mlsanity.com/paper/2106.06130/) (2021)
- [SAVi++: Towards End-to-End Object-Centric Learning from Real-World Videos](https://mlsanity.com/paper/2206.07764/) (2022)
- [Physion: Evaluating Physical Prediction from Vision in Humans and Machines](https://mlsanity.com/paper/2106.08261/) (2021)
- [SlotFormer: Unsupervised Visual Dynamics Simulation with Object-Centric Models](https://mlsanity.com/paper/2210.05861/) (2022)
- [Simple Unsupervised Object-Centric Learning for Complex and Naturalistic Videos](https://mlsanity.com/paper/2205.14065/) (2022)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [Principled Simplicial Neural Networks for Trajectory Prediction](https://mlsanity.com/paper/2102.10058/) (2021)
- [Propagation Networks for Model-Based Control Under Partial Observation](https://mlsanity.com/paper/1809.11169/) (2018)
- [The physics of higher-order interactions in complex systems](https://mlsanity.com/paper/2110.06023/) (2021)
- [ComPhy: Compositional Physical Reasoning of Objects and Events from Videos](https://mlsanity.com/paper/2205.01089/) (2022)
- [Attention over learned object embeddings enables complex visual reasoning](https://mlsanity.com/paper/2012.08508/) (2020)
- [Learning rigid dynamics with face interaction graph networks](https://mlsanity.com/paper/2212.03574/) (2022)
- [Learning Physical Dynamics with Subequivariant Graph Neural Networks](https://mlsanity.com/paper/2210.06876/) (2022)
- [Geometric deep learning reveals the spatiotemporal fingerprint of microscopic motion](https://mlsanity.com/paper/2202.06355/) (2022)
- [Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes](https://mlsanity.com/paper/2203.03060/) (2022)

## Built on by (most cited first, 5 of 5)

- [Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamics](https://mlsanity.com/paper/2511.08185/) (2025)
- [RigidFormer: Learning Rigid Dynamics using Transformers](https://mlsanity.com/paper/2605.09196/) (2026)
- [PhysiFormer: Learning to Simulate Mechanics in World Space](https://mlsanity.com/paper/2606.27364/) (2026)
- [Learning Contact Dynamics through Touching: Action-conditional Graph Neural Networks for Robotic Peg Insertion](https://mlsanity.com/paper/2509.12151/) (2025)
- [Physics-informed Diffusion Generative Model for Time-Series Data Synthesis in Dynamic Systems](https://mlsanity.com/paper/2608.10941/) (2026)

## Abstract (arXiv)

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.