  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.
