Sparsely constrained neural networks for model discovery of PDEs

• URL: http://arxiv.org/abs/2011.04336v2
• Date: Tue, 4 May 2021 12:23:38 GMT
• Title: Sparsely constrained neural networks for model discovery of PDEs
• Authors: Gert-Jan Both, Gijs Vermarien, Remy Kusters
• Abstract summary: We present a modular framework that determines the sparsity pattern of a deep-learning based surrogate using any sparse regression technique. We show how a different network architecture and sparsity estimator improve model discovery accuracy and convergence on several benchmark examples.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 \url{https://github.com/PhIMaL/DeePyMoD}

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