# Deep splitting method for parabolic PDEs

## TL;DR

This paper presents a novel deep learning-based operator splitting method for solving high-dimensional nonlinear parabolic PDEs efficiently, demonstrated on physics, finance, and control problems.

## Contribution

It introduces a new numerical approach combining operator splitting with deep learning to handle extremely high-dimensional PDEs effectively.

## Key findings

- Successfully solves PDEs in up to 10,000 dimensions
- Achieves very good accuracy with short computation times
- Applicable to physics, stochastic control, and finance problems

## 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.