  Simulating rigid collisions among arbitrary shapes is notoriously difficult
due to complex geometry and the strong non-linearity of the interactions. While
graph neural network (GNN)-based models are effective at learning to simulate
complex physical dynamics, such as fluids, cloth and articulated bodies, they
have been less effective and efficient on rigid-body physics, except with very
simple shapes. Existing methods that model collisions through the meshes' nodes
are often inaccurate because they struggle when collisions occur on faces far
from nodes. Alternative approaches that represent the geometry densely with
many particles are prohibitively expensive for complex shapes. Here we
introduce the Face Interaction Graph Network (FIGNet) which extends beyond
GNN-based methods, and computes interactions between mesh faces, rather than
nodes. Compared to learned node- and particle-based methods, FIGNet is around
4x more accurate in simulating complex shape interactions, while also 8x more
computationally efficient on sparse, rigid meshes. Moreover, FIGNet can learn
frictional dynamics directly from real-world data, and can be more accurate
than analytical solvers given modest amounts of training data. FIGNet
represents a key step forward in one of the few remaining physical domains
which have seen little competition from learned simulators, and offers allied
fields such as robotics, graphics and mechanical design a new tool for
simulation and model-based planning.
