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Nonlinear integro-differential operator regression with neural networks (1810.08552v1)
Published 19 Oct 2018 in cs.LG, physics.comp-ph, physics.data-an, and stat.ML
Abstract: This note introduces a regression technique for finding a class of nonlinear integro-differential operators from data. The method parametrizes the spatial operator with neural networks and Fourier transforms such that it can fit a class of nonlinear operators without needing a library of a priori selected operators. We verify that this method can recover the spatial operators in the fractional heat equation and the Kuramoto-Sivashinsky equation from numerical solutions of the equations.
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