Benchmarking Optimizers to Solve Inverse Problems with Differentiable Physics Simulators
Xiang Chen, Huanhuan Xia
Abstract
Solving inverse problems with differentiable physics simulators holds the potential to revolutionize scientific discovery and engineering design, as it enjoys both the strict physical correctness from rigorous numerical physics simulators, and the high efficiency and effectiveness from automatic differentiation and gradient-based optimization. However, currently, this paradigm faces performance issues in optimization. In this work, we target benchmarking the performance of different optimizers to solve various inverse problems. We construct 12 differentiable physics simulators spanning physics domains including discrete mechanics, continuous mechanics, atomistic simulations, rendering, and semi-empirical physics models. Based on these simulators, we design corresponding inverse problems that can be categorized into parameter identification, inverse design, and optimal control. Finally, we conduct extensive experiments to compare the performance of different optimizers, including regular first-order methods, approximate second-order methods, as well as global optimizers, on these inverse problems, and analyze the results to provide insights on how to choose and design optimizers for differentiable programming. We hope such benchmarks can inspire the development of more effective optimizers, and further promote the applications of differentiable programming in various scientific and engineering domains.