  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.
