Boundary Integral

Boundary integral methods offer powerful techniques for solving partial differential equations (PDEs), particularly those with complex geometries or boundary conditions, by transforming the problem into an integral equation defined only on the boundary. Current research emphasizes the integration of these methods with deep learning, employing neural networks (e.g., deep operator networks, boundary integral neural networks) to learn solution operators or Green's functions, thereby improving efficiency and generalizability across diverse domains and PDE types. This approach promises significant advancements in computational mechanics, inverse problems, and other fields requiring the solution of PDEs, offering faster and more robust solutions compared to traditional numerical methods.