Nonlinear integro-differential operator regression with neural networks

Olivier Desjardins; Ravi G. Patel

Nonlinear integro-differential operator regression with neural networks

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arxiv 1810.08552 v1 pith:U5NJ4B2A submitted 2018-10-19 cs.LG physics.comp-phphysics.data-anstat.ML

Ravi G. Patel , Olivier Desjardins This is my paper · ORCID

classification cs.LGphysics.comp-phphysics.data-anstat.ML

keywords operatorsnonlinearclassequationintegro-differentialmethodnetworksneural

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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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