Boundary Integral Network

Boundary Integral Networks (BINs) are a novel class of neural networks designed to solve partial differential equations (PDEs) by leveraging boundary integral formulations. Current research focuses on developing efficient algorithms, such as those employing radial basis functions, to learn Green's functions—fundamental solutions to PDEs—or directly solve boundary integral equations using neural network approximations. This approach offers advantages over traditional methods by reducing dimensionality, simplifying boundary condition handling, and enabling efficient solutions for complex geometries and unbounded domains, with applications in diverse fields like computational mechanics and groundwater flow modeling.