Deep splitting method for parabolic PDEs

Deep splitting method for parabolic PDEs

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,...

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Bibliographic Details
Main Authors: Beck, Christian, Becker, Sebastian, Cheridito, Patrick, Jentzen, Arnulf, Neufeld, Ariel
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2022
Subjects:
Science::Mathematics
Nonlinear Partial Differential Equations
Splitting-Up Method
Online Access:https://hdl.handle.net/10356/153744
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Institution: Nanyang Technological University
Language: English
Description
Summary: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.

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