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arXiv · 1810.08552

Nonlinear integro-differential operator regression with neural networks

Ravi G. Patel·Olivier Desjardins
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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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BibTeXRIS

Ravi G. Patel, Olivier Desjardins. 2018-10-19. Nonlinear integro-differential operator regression with neural networks. https://arxiv.org/abs/1810.08552

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