Sparsely constrained neural networks for model discovery of PDEs

2020/11/09 by Both, Gert-Jan, Vermarien, Gijs, Kusters, Remy
#Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG)

paper · doi:10.48550/arxiv.2011.04336

Abstract

Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model discovery to densely sampled data-sets with low noise. Neural network-based approaches circumvent this limit by constructing a surrogate model of the data, but have to date ignored advances in sparse regression algorithms. In this paper we present a modular framework that dynamically determines the sparsity pattern of a deep-learning based surrogate using any sparse regression technique. Using our new approach, we introduce a new constraint on the neural network and show how a different network architecture and sparsity estimator improve model discovery accuracy and convergence on several benchmark examples. Our framework is available at \urlhttps://github.com/PhIMaL/DeePyMoD

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