Deep Ritz Method

The Deep Ritz Method (DRM) leverages neural networks to solve partial differential equations (PDEs) by directly minimizing a variational formulation, offering a potentially powerful alternative to traditional numerical methods. Current research focuses on improving the method's efficiency and accuracy through techniques like multi-level domain decomposition, adaptive sampling strategies, and incorporating specialized network architectures to handle specific PDE characteristics, such as singularities or high dimensionality. These advancements aim to enhance the scalability and reliability of DRM for solving complex PDEs arising in diverse scientific and engineering applications, ultimately improving the accuracy and efficiency of simulations across various fields.