Simulating the time evolution of physical systems is pivotal in many
scientific and engineering problems. An open challenge in simulating such
systems is their multi-resolution dynamics: a small fraction of the system is
extremely dynamic, and requires very fine-grained resolution, while a majority
of the system is changing slowly and can be modeled by coarser spatial scales.
Typical learning-based surrogate models use a uniform spatial scale, which
needs to resolve to the finest required scale and can waste a huge compute to
achieve required accuracy. In this work, we introduce Learning controllable
Adaptive simulation for Multi-resolution Physics (LAMP) as the first full deep
learning-based surrogate model that jointly learns the evolution model and
optimizes appropriate spatial resolutions that devote more compute to the
highly dynamic regions. LAMP consists of a Graph Neural Network (GNN) for
learning the forward evolution, and a GNN-based actor-critic for learning the
policy of spatial refinement and coarsening. We introduce learning techniques
that optimizes LAMP with weighted sum of error and computational cost as
objective, allowing LAMP to adapt to varying relative importance of error vs.
computation tradeoff at inference time. We evaluate our method in a 1D
benchmark of nonlinear PDEs and a challenging 2D mesh-based simulation. We
demonstrate that our LAMP outperforms state-of-the-art deep learning surrogate
models, and can adaptively trade-off computation to improve long-term
prediction error: it achieves an average of 33.7% error reduction for 1D
nonlinear PDEs, and outperforms MeshGraphNets + classical Adaptive Mesh
Refinement (AMR) in 2D mesh-based simulations. Project website with data and
code can be found at: http://snap.stanford.edu/lamp.Comment: ICLR 2023, notable top-25% (spotlight), 19 pages, 9 figure