Boundary-Integral Type Neural Network (BINN) for Flow Problems in Anisotropic Reservoirs

Abstract Accurate simulation of fluid flow in anisotropic reservoirs is challenging for traditional numerical methods and physics-informed neural networks (PINNs) due to issues with complex geometries, singularities, and scalability. This study introduces a Boundary-Integral Neural Network (BINN) framework that merges boundary integral equations (BIEs) with deep learning for 2D single-phase flow in anisotropic reservoirs. By converting governing partial differential equations into boundary-only integral equations via Green's functions, BINN focuses neural network learning on boundary unknowns (e.g., pressure and normal derivatives), reconstructing domain solutions through boundary integrals. This reduces dimensionality, avoids global sampling costs of PINNs, enforces boundary conditions analytically, and handles singularities near wells/fractures via Green's function kernels. Three examples validate BINN: flow with full-tensor permeability in a rectangle, single-well-induced pressure singularities, and multi-well flow in an irregular trapezoidal domain. Results align closely with boundary element method (BEM) solutions, with RMSEs of 5.17×10−4 MPa for single-well cases and <10−3 MPa for complex scenarios. BINN shows stable convergence across geometric irregularities and anisotropic effects, demonstrating robustness in capturing flow physics under coupled influences of tensor permeability, source-sink terms, and complex boundaries. This work positions BINN as a promising meshless approach for anisotropic reservoir simulation.