Momentum-Conserving Graph Neural Networks for Deformable Objects

Jiahong Wang, Logan Numerow, Stelian Coros, Christian Theobalt, Vahid Babaei, Bernhard Thomaszewski

Keywords: Graph neural networks, Momentum conservation, Physical simulation, Deformable objects

TL;DR: We propose a novel GNN architecture that accurately tracks and automatically conserves linear and angular momentum by design for physical simulations of deformable objects.

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.

Submission Number: 240