Solving stochastic partial differential equations using neural networks in the Wiener chaos expansion
Machine Learning
2026-01-27 v2 Machine Learning
Numerical Analysis
Numerical Analysis
Probability
Abstract
In this paper, we solve stochastic partial differential equations (SPDEs) numerically by using (possibly random) neural networks in the truncated Wiener chaos expansion of their corresponding solution. Moreover, we provide some approximation rates for learning the solution of SPDEs with additive and/or multiplicative noise. Finally, we apply our results in numerical examples to approximate the solution of three SPDEs: the stochastic heat equation, the Heath-Jarrow-Morton equation, and the Zakai equation.
Keywords
Cite
@article{arxiv.2411.03384,
title = {Solving stochastic partial differential equations using neural networks in the Wiener chaos expansion},
author = {Ariel Neufeld and Philipp Schmocker},
journal= {arXiv preprint arXiv:2411.03384},
year = {2026}
}