Scale-invariant Learning by Physics Inversion
This addresses a bottleneck for researchers and practitioners in scientific fields relying on machine learning for parameter estimation and optimal control, though it appears incremental as it builds on existing methods.
The paper tackles the problem of suboptimal optimization in inverse problems involving physical processes due to strongly varying gradients, proposing a hybrid training approach that yields significant improvements on a range of optimization and learning tasks.
Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse problems. We find that state-of-the-art training techniques are not well-suited to many problems that involve physical processes. The highly nonlinear behavior, common in physical processes, results in strongly varying gradients that lead first-order optimizers like SGD or Adam to compute suboptimal optimization directions. We propose a novel hybrid training approach that combines higher-order optimization methods with machine learning techniques. We take updates from a scale-invariant inverse problem solver and embed them into the gradient-descent-based learning pipeline, replacing the regular gradient of the physical process. We demonstrate the capabilities of our method on a variety of canonical physical systems, showing that it yields significant improvements on a wide range of optimization and learning problems.