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

2024-11-18

AI Summary

Long-term prediction of complex multi-body collisions in rigid-body dynamics remains challenging, with existing graph neural networks (GNNs) exhibiting significant limitations in modeling long-range interactions and generalizing across diverse geometric configurations and initial conditions. Method: We propose a novel physics-informed neural dynamics model that integrates physical priors with high-order topological structures. Specifically, we introduce simplicial complex embeddings into neural networks to enable topology-aware, physically constrained message passing, and jointly regularize the model using rigid-body dynamical equations and physics-informed neural networks (PINNs). Contribution/Results: Our approach achieves substantial improvements in long-horizon rollout accuracy and demonstrates strong generalization to unseen geometries and initial states. By embedding domain knowledge—both physical laws and topological relationships—into the architecture, the model yields interpretable, robust, and broadly applicable simulations for multi-body systems, establishing a generalizable and explainable paradigm for neural dynamical modeling.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Deep Neural Architectures and Foundation Models
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

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.

Problem

• Modeling rigid body dynamics with complex interactions
• Improving long-term predictions in collision simulations
• Generalizing to unseen multi-entity dynamic scenarios

Innovation

• Incorporates higher-order topology complexes for representation
• Uses physics-informed message-passing neural architecture
• Embeds physical laws directly in the model