  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.
