Radial Buckley-Leverett Solver Based on Physics-Informed Neural Networks with Gated Attention Mechanism

In oilfield production optimization, water flooding is a key technique to enhance recovery, and its seepage process is commonly modeled by the Buckley-Leverett (BL) equation. However, under planar radial flow conditions, the BL equation is challenging to solve due to its hyperbolic nature and shock formation. Traditional numerical methods arc constrained by numerical dissipation and high computational costs, limiting predictive accuracy, while conventional physics-informed neural networks (PINNs) suffer from unstable convergence near shocks, leading to poor accuracy. To address these challenges, this paper proposes a PINN framework integrated with a gated attention mechanism (Gated Attention-PINN). By introducing gated attention modules, the method strengthens feature interactions, significantly improves shock-capturing capability and convergence stability, and further enhances model interpretability. This work not only extends the applicability of PINNs to radial flow simulations but also provides a high-accuracv, stable, and interpretable tool for complex multiphase flow modeling. Experimental results demonstrate that Gated Attention-PINN outperforms standard PINN in both accuracy and convergence speed, achieving a 65% reduction in mean squared error and an increase in R2 to over 95%.