Momentum-Conserving Graph Neural Networks for Deformable Objects

2026-04-28

AI Summary

Existing graph neural networks struggle to enforce conservation of linear and angular momentum when simulating deformable objects. This work proposes MomentumGNN, the first architecture that guarantees strict momentum conservation through a constructive design at the architectural level: instead of directly predicting nodal accelerations, it predicts stretching and bending impulses on edges, combined with a physics-informed unsupervised loss for training. By embedding physical conservation laws into the network structure, MomentumGNN achieves significantly improved accuracy and stability in momentum-sensitive simulation scenarios, outperforming current baselines across multiple benchmarks.

Abstract

Graph neural networks (GNNs) have emerged as a versatile and efficient option for modeling the dynamic behavior of deformable materials. While GNNs generalize readily to arbitrary shapes, mesh topologies, and material parameters, existing architectures struggle to correctly predict the temporal evolution of key physical quantities such as linear and angular momentum. In this work, we propose MomentumGNN -- a novel architecture designed to accurately track momentum by construction. Unlike existing GNNs that output unconstrained nodal accelerations, our model predicts per-edge stretching and bending impulses which guarantee the preservation of linear and angular momentum. We train our network in an unsupervised fashion using a physics-based loss, and we show that our method outperforms baselines in a number of common scenarios where momentum plays a pivotal role.

Problem

• momentum conservation
• graph neural networks
• deformable objects
• physical simulation

Innovation

• Momentum Conservation
• Graph Neural Networks
• Deformable Objects
• Physics-Based Learning
• Unsupervised Training