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 sequence of separate learning problems. Since computational graph each subproblems is comparatively small, approach can handle extremely high-dimensional PDEs. We test on different examples from physics, stochastic control and mathematical finance. all cases, it yields very good results in up to 10,000 dimensions short run times.