A physics-informed adaptive radial basis neural network (PIARNN) for fractured horizontal well simulation

Multistage fractured horizontal wells are widely applied to develop low-permeability reservoirs, where precise numerical simulation plays a vital role in reservoir management. However, the governing equations of such fractured systems exhibit strong nonlinearity and are typically solved using the Newton–Raphson method. This approach requires repeated assembly and inversion of large Jacobian matrices, resulting in prohibitive computational cost. Recently, physics-informed neural networks (PINNs) have emerged as a promising approach for solving nonlinear partial differential equations. Nevertheless, most existing PINN-based methods focus on vertical well scenarios and directly learn the full pressure field, which limits computational efficiency. To address these limitations, this paper proposes a physics-informed adaptive radial basis neural network (PIARNN) for fractured horizontal wells simulation. The method achieves Newton-level accuracy without explicit Jacobian computation. Specifically, the Embedded Discrete Fracture Model (EDFM) is discretized and incorporated into the loss function to impose physical constraints. An adaptive factor is introduced, and a dual-branch architecture is designed to independently characterize matrix and fracture pressure dynamics. Furthermore, radial basis functions are used for feature mapping, and model learns pressure increments at the next time step to approximate the Newton iteration updates. Three reservoir cases are used for model validation. The results demonstrate that PIARNN can accurately predict pressure fields and bottomhole pressure responses with errors stabilized at the order of 10⁻⁵. The model exhibits adaptability to both hydraulic fractures and discrete natural fractures. Compared with existing PINN and PICNN methods, PIARNN achieves higher accuracy and superior stability in complex fracture systems. This study provides a promising alternative to traditional Newton-based solvers for nonlinear seepage problems in low-permeability reservoirs.