Accelerating Particle and Fluid Simulations with Differentiable Graph Networks for Solving Forward and Inverse Problems

TL;DR

This paper introduces differentiable graph network simulators (GNS) that leverage physics embedding to accelerate particle and fluid simulations, enabling efficient forward modeling and inverse problem solving with significant speedups and improved generalization.

Contribution

The paper presents a novel physics-embedded differentiable graph network simulator (GNS) and a hybrid GNS/MPM approach, enabling fast, accurate simulations and inverse problem solutions for particulate and fluid dynamics.

Findings

GNS achieves over 165x speedup in granular flow prediction.

Hybrid GNS/MPM accelerates forward simulations by 24x while satisfying conservation laws.

Differentiable GNS successfully solves inverse problems by identifying material parameters.

Abstract

We leverage physics-embedded differentiable graph network simulators (GNS) to accelerate particulate and fluid simulations to solve forward and inverse problems. GNS represents the domain as a graph with particles as nodes and learned interactions as edges. Compared to modeling global dynamics, GNS enables learning local interaction laws through edge messages, improving its generalization to new environments. GNS achieves over 165x speedup for granular flow prediction compared to parallel CPU numerical simulations. We propose a novel hybrid GNS/Material Point Method (MPM) to accelerate forward simulations by minimizing error on a pure surrogate model by interleaving MPM in GNS rollouts to satisfy conservation laws and minimize errors achieving 24x speedup compared to pure numerical simulations. The differentiable GNS enables solving inverse problems through automatic differentiation, identifying material parameters that result in target runout distances. We demonstrate the ability of GNS to solve inverse problems by iteratively updating the friction angle (a material property) by computing the gradient of a loss function based on the final and target runouts, thereby identifying the friction angle that best matches the observed runout. The physics-embedded and differentiable simulators open an exciting new paradigm for AI-accelerated design, control, and optimization.