Numerical wave propagation aided by deep learning

Duration: 50 mins 17 secs

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Description:	Richard Tsai 8 March 2022 – 13:30 to 14:15


Created:	2022-03-14 13:35
Collection:	Frontiers in analysis of kinetic equations
Publisher:	Isaac Newton Institute
Copyright:	Richard Tsai
Language:	eng (English)


Abstract:	We first discuss the questions: “what should one learn?” And “In which (scientific computing) context does it make sense?" We propose a deep learning approach for wave propagation in media with multiscale wave speed, using a second-order linear wave equation model as a proof-of-concept. We use neural networks to enhance the accuracy of a given inaccurate coarse solver, which under-resolves a class of multiscale wave media and wave fields of interest. We discuss the generation of suitable training data and compare the performance of networks trained by different data sets. We find that the trained neural networks can approximate the nonlinear dependence of the propagation on the wave speed as long as the causality is appropriately sampled in training data. We combine the neural-network-enhanced coarse solver with the parareal algorithm and demonstrate that the coupled approach improves the stability of parareal algorithms for wave propagation and improves the accuracy of the enhanced coarse solvers.

Abstract:

We first discuss the questions: “what should one learn?” And “In which (scientific computing) context does it make sense?" We propose a deep learning approach for wave propagation in media with multiscale wave speed, using a second-order linear wave equation model as a proof-of-concept. We use neural networks to enhance the accuracy of a given inaccurate coarse solver, which under-resolves a class of multiscale wave media and wave fields of interest. We discuss the generation of suitable training data and compare the performance of networks trained by different data sets. We find that the trained neural networks can approximate the nonlinear dependence of the propagation on the wave speed as long as the causality is appropriately sampled in training data. We combine the neural-network-enhanced coarse solver with the parareal algorithm and demonstrate that the coupled approach improves the stability of parareal algorithms for wave propagation and improves the accuracy of the enhanced coarse solvers.

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