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Deep splitting method for parabolic PDEs

by Ch. Beck and S. Becker and P. Cheridito and A. Jentzen and A. Neufeld

(Report number 2019-39)

Abstract
In this paper we introduce a numerical method for 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.

Keywords:

@Techreport{BBCJN19_843,
  author = {Ch. Beck and S. Becker and P. Cheridito and A. Jentzen and A. Neufeld},
  title = {Deep splitting method for parabolic PDEs},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2019-39},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2019/2019-39.pdf },
  year = {2019}
}

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