Dynami-CAL GraphNet: A Physics-Informed Graph Neural Network Conserving Linear and Angular Momentum for Dynamical Systems

2025-01-13

AI Summary

Addressing the challenge of simultaneously achieving accuracy, generality, and computational efficiency in modeling multi-body dynamical systems, this paper proposes a physics-conservation-driven graph neural network (PC-GNN). Methodologically, it introduces edge-wise local rotation-equivariant reference frames to rigorously encode paired conservation laws for linear and angular momentum; further, it outputs interpretable, edge-level impulses—enabling robust modeling of heterogeneous interactions and external forces. By integrating physics-informed constraints and equivariant geometric representations, PC-GNN achieves stable long-horizon rollout error and effective cross-configuration extrapolation on 3D granular systems. Results demonstrate significant improvements in physical consistency and prediction accuracy, while maintaining real-time inference capability, interpretability, and strong generalization across unseen system configurations.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Low Level & Physics-based Vision
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Accurate, interpretable, and real-time modeling of multi-body dynamical systems is essential for predicting behaviors and inferring physical properties in natural and engineered environments. Traditional physics-based models face scalability challenges and are computationally demanding, while data-driven approaches like Graph Neural Networks (GNNs) often lack physical consistency, interpretability, and generalization. In this paper, we propose Dynami-CAL GraphNet, a Physics-Informed Graph Neural Network that integrates the learning capabilities of GNNs with physics-based inductive biases to address these limitations. Dynami-CAL GraphNet enforces pairwise conservation of linear and angular momentum for interacting nodes using edge-local reference frames that are equivariant to rotational symmetries, invariant to translations, and equivariant to node permutations. This design ensures physically consistent predictions of node dynamics while offering interpretable, edge-wise linear and angular impulses resulting from pairwise interactions. Evaluated on a 3D granular system with inelastic collisions, Dynami-CAL GraphNet demonstrates stable error accumulation over extended rollouts, effective extrapolations to unseen configurations, and robust handling of heterogeneous interactions and external forces. Dynami-CAL GraphNet offers significant advantages in fields requiring accurate, interpretable, and real-time modeling of complex multi-body dynamical systems, such as robotics, aerospace engineering, and materials science. By providing physically consistent and scalable predictions that adhere to fundamental conservation laws, it enables the inference of forces and moments while efficiently handling heterogeneous interactions and external forces.

Problem

• Multi-body Dynamical Systems
• Prediction Accuracy
• Computational Efficiency

Innovation

• Dynami-CAL GraphNet
• Physics-Informed Learning
• Multi-Body Dynamics Prediction