Momentum-Conserving Graph Neural Networks for Deformable Objects

TL;DR

This paper introduces MomentumGNN, a graph neural network architecture that inherently conserves momentum, improving the modeling of deformable objects' physical behavior.

Contribution

The paper presents a novel GNN architecture that predicts impulses to ensure momentum conservation, addressing a key limitation of previous models.

Findings

MomentumGNN outperforms baselines in momentum-sensitive scenarios.

The model accurately predicts physical quantities like linear and angular momentum.

Unsupervised training with physics-based loss is effective for this task.

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.