Sparsely constrained neural networks for model discovery of PDEs

Sparse regression on a library of candidate features has developed as the prime method to discover the PDE underlying a spatio-temporal dataset. As these features consist of higher order derivatives, model discovery is typically limited to low-noise and dense datasets due to the erros inherent to numerical differentiation. Neural network-based approaches circumvent this limit, but to date have ignored advances in sparse regression algorithms. In this paper we present a modular framework that combines deep-learning based approaches with an arbitrary sparse regression technique. We demonstrate with several examples that this combination facilitates and enhances model discovery tasks. We release our framework as a package at https://github.com/PhIMaL/DeePyMoD