Benchmarking optimizers for physics based inverse problems in engineering
Benchmarking Optimizers to Solve Inverse Problems with Differentiable Physics Simulators
Machine Learning
Summary
Solving problems by working backwards from desired results using physics simulations can greatly improve how scientists and engineers design things. The authors compared many different mathematical methods for finding best solutions when using these simulations. They tested 12 different physics scenarios and categorized problems into figuring out unknown parameters, designing objects, and controlling systems. Their experiments help guide others in choosing the best optimization methods for these tasks.
What this means in practice
- •For mechanical engineers: Optimize mechanical system designs using physics-based simulators with improved optimizer selection for faster and more accurate results.
- •For computer graphics developers: Improve inverse rendering tasks by choosing suitable optimizers based on benchmarked performance on differentiable physics simulators.
Authors
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.