Deep splitting method for parabolic PDEs
Numerical Analysis
2021-10-12 v2 Machine Learning
Numerical Analysis
Probability
Machine Learning
Abstract
In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational graph for each of the subproblems is comparatively small, the approach can handle extremely high-dimensional PDEs. We test the method on different examples from physics, stochastic control and mathematical finance. In all cases, it yields very good results in up to 10,000 dimensions with short run times.
Cite
@article{arxiv.1907.03452,
title = {Deep splitting method for parabolic PDEs},
author = {Christian Beck and Sebastian Becker and Patrick Cheridito and Arnulf Jentzen and Ariel Neufeld},
journal= {arXiv preprint arXiv:1907.03452},
year = {2021}
}
Comments
25 pages