Learning Mesh-Based Simulation with Graph Networks

TL;DR

MeshGraphNets leverage graph neural networks to efficiently learn and simulate complex physical systems on meshes, adapting resolution and scaling to diverse scientific applications with high accuracy and speed.

Contribution

Introduces MeshGraphNets, a novel framework for mesh-based simulation using graph neural networks that supports adaptive mesh resolution and scalable, accurate predictions across various physical systems.

Findings

Accurately predicts dynamics of physical systems like aerodynamics and cloth.

Runs 10-100 times faster than traditional simulations.

Supports adaptive mesh discretization during simulation.

Abstract

Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike favorable trade-offs between accuracy and efficiency. However, high-dimensional scientific simulations are very expensive to run, and solvers and parameters must often be tuned individually to each system studied. Here we introduce MeshGraphNets, a framework for learning mesh-based simulations using graph neural networks. Our model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation. Our results show it can accurately predict the dynamics of a wide range of physical systems, including aerodynamics, structural mechanics, and cloth. The model's adaptivity supports learning resolution-independent dynamics and can scale to more complex state spaces at test time. Our method is also highly efficient, running 1-2 orders of magnitude faster than the simulation on which it is trained. Our approach broadens the range of problems on which neural network simulators can operate and promises to improve the efficiency of complex, scientific modeling tasks.