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Title: Deep splitting method for parabolic PDEs
Authors: Beck, Christian
Becker, Sebastian
Cheridito, Patrick
Jentzen, Arnulf
Neufeld, Ariel
Keywords: Science::Mathematics
Issue Date: 2021
Source: Beck, C., Becker, S., Cheridito, P., Jentzen, A. & Neufeld, A. (2021). Deep splitting method for parabolic PDEs. SIAM Journal On Scientific Computing, 43(5), A3135-A3154.
Journal: SIAM Journal on Scientific Computing
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.
ISSN: 1064-8275
DOI: 10.1137/19M1297919
Rights: © 2021 Society for Industrial and Applied Mathematics. All rights reserved. This paper was published in SIAM Journal on Scientific Computing and is made available with permission of Society for Industrial and Applied Mathematics.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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