Nonlinear integro-differential operator regression with neural networks
Machine Learning
2018-10-22 v1 Computational Physics
Data Analysis, Statistics and Probability
Machine Learning
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.
Cite
@article{arxiv.1810.08552,
title = {Nonlinear integro-differential operator regression with neural networks},
author = {Ravi G. Patel and Olivier Desjardins},
journal= {arXiv preprint arXiv:1810.08552},
year = {2018}
}
Comments
5 pages, 3 figures, preprint submitted to the Journal of Computational Physics