Accelerating Particle and Fluid Simulations with Differentiable Graph
  Networks for Solving Forward and Inverse Problems
Krishna Kumar Yongjin Choi
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.