Sparsely constrained neural networks for model discovery of PDEs

11/09/2020
by   Gert-Jan Both, et al.
16

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

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Code Repositories

DeePyMoD

DeepMod is a deep learning based model discovery algorithm which seeks the partial differential equation underlying a spatio-temporal data set. DeepMoD employs sparse regression on a library of basis functions and their corresponding spatial derivatives. This code is based on the paper: [arXiv:1904.09406](http://arxiv.org/abs/1904.09406)


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