¹1Physical Science and Engineering (PSE) Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia
²School of Petroleum Engineering, Yangtze University, Wuhan, Hubei, China
³State Key Laboratory of Low Carbon Catalysis and Carbon Dioxide Utilization (Yangtze University), Wuhan 430100, China.

⁴Saudi Aramco, Dhahran, Saudi Arabia.

^*Correspondence: Xiang Rao, Email: raoxiang0103@163.com

AESIG, 2025, 1(1), 80-94;

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This research was no funding provided.

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Abstract

This study pioneers the application of Boundary-Integral Neural Networks (BINNs) to subsurface flow simulation, addressing steady-state single-phase flow governed by Laplace-type equations in hydrocarbon reservoirs. BINNs synergistically integrate boundary integral equations (BIEs) with deep learning to overcome limitations of traditional mesh-based methods and Physics-Informed Neural Networks (PINNs). By leveraging Green’s functions, BINNs transform partial differential equations into boundary-only formulations, where neural networks exclusively approximate boundary unknowns (pressure/flux), and interior solutions are reconstructed analytically. This approach achieves intrinsic dimensionality reduction, eliminating spatial domain discretization while ensuring mathematical consistency through exact boundary condition enforcement. Numerical validation demonstrates BINNs’ computational advantages: In a rectangular reservoir, BINNs achieve sub-0.01% relative error (4.80×10−4 MPa) at interior points. For a complex trapezoidal reservoir with geometric singularities, BINNs attain Boundary Element Method (BEM)-comparable accuracy (max error ~0.115MPa) without specialized singularity treatments. Furthermore, in a challenging non-convex domain featuring recessed boundaries and internal production wells, BINNs effectively resolve the pressure singularities near wellbores, achieving high-fidelity reconstruction with a maximum relative error of 0.32%. The method’s efficiency is evidenced by rapid convergence with minimal boundary sampling and moderate network sizes. BINNs provide a robust, meshless paradigm for reservoir-scale simulation, effectively handling irregular geometries while maintaining high fidelity and scalability, which uncovers its remarkable computational capabilities in the realm of single-phase flow, and offers an inaugural investigation and benchmark for its prospective extensive utilization in numerical reservoir simulations.

Keywords: Deep Learning; Boundary integral equations (BIEs); Physics-informed neural networks (PINNs); Boundary-Integral Neural Networks(BINNs); Meshless Reservoir Simulation; Dimensionality Reduction

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