Deep Galerkin Method

The Deep Galerkin Method (DGM) leverages deep neural networks to solve differential equations, particularly challenging high-dimensional partial differential equations (PDEs) where traditional methods struggle. Current research focuses on improving DGM's efficiency and accuracy through techniques like adaptive sampling, randomized sparse updates, and the development of novel architectures to ensure conservation laws and handle various boundary conditions. This approach offers a powerful alternative for solving complex PDEs arising in diverse scientific and engineering domains, potentially accelerating simulations and enabling the study of previously intractable problems.