Neural Multigrid

Neural multigrid methods combine the efficiency of multigrid algorithms for solving partial differential equations (PDEs) with the learning capabilities of neural networks. Current research focuses on developing novel architectures, such as multigrid neural operators (MgNOs) and variations of U-Nets integrated with multigrid principles, to improve accuracy and efficiency in solving PDEs across diverse applications, including fluid dynamics, porous media flow, and medical image segmentation. These advancements offer significant potential for accelerating simulations and enhancing the accuracy of data-driven models in scientific computing and engineering, particularly for problems involving complex geometries and multiscale phenomena.