Global Convergence of Deep Galerkin and PINNs Methods for Solving Partial Differential Equations

Understand

Numerically solving high-dimensional partial differential equations (PDEs) is a major challenge.

• Conventional methods, such as finite difference methods, are unable to solve high-dimensional PDEs due to the curse-of-dimensionality.
• A variety of deep learning methods have been recently developed to try and solve high-dimensional PDEs by approximating the solution using a neural network.
• In this paper, we prove global convergence for one of the commonly-used deep learning algorithms for solving PDEs, the Deep Galerkin Method (DGM).