Learning structured representations for accelerating scientific discovery and simulation

In this talk, I will present my work on developing machine learning methods for scientific discovery and simulation. In scientific discovery, discovering universal, simple laws from multiple dynamical systems is critical across many scientific disciplines. I introduce a paradigm and method for learning theories, where instead of using one model to learn everything, a theory parsimoniously predicts one aspect of the dynamics and the domain in which these predictions are accurate. By incorporating four important inductive biases from how physicists model the world (divide-and-conquer, Occam’s razor, unification, and lifelong learning), our method achieves significantly better accuracy, interpretability and sample efficiency.

Secondly, across most disciplines of science, e.g., physics, biomedicine, materials, mechanical engineering, and energy, a most critical challenge is that their simulations are typically slow due to the complex and multi-resolution nature of the system. I introduce Learning controllable Adaptive simulation for Multi-resolution Physics (LAMP), the first deep learning-based surrogate model that learns the evolution model while optimizing spatial resolutions to allocate more computation to highly dynamic regions. LAMP includes a Graph Neural Network (GNN)-based evolution model to learn the forward dynamics and a GNN-based actor-critic to learn the policy of discrete actions of local refinement and coarsening of the spatial mesh, trained via reinforcement learning. Our experiments on 1D PDEs and 2D mesh-based simulations demonstrate LAMP’s superior performance compared to state-of-the-art surrogate models combined with Adaptive Mesh Refinement.

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