Deep splitting method for parabolic PDEs
This method addresses the computational challenge of high-dimensional PDEs for applications in physics, stochastic control, and mathematical finance, representing a novel approach rather than an incremental improvement.
The authors tackled the problem of solving high-dimensional nonlinear parabolic PDEs by introducing a numerical method that combines operator splitting with deep learning, achieving very good results in up to 10,000 dimensions with short run times.
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.