Deep Splitting Method for Parabolic PDEs

TLDR

The method’s small computational graphs enable it to handle extremely high-dimensional PDEs. The paper introduces a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning. The method splits the PDE approximation into a sequence of separate learning problems and is tested on physics, stochastic control, and finance examples. The method achieves very good results up to 10,000 dimensions with short run times.

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.