Physics-Informed Generative Adversarial Network Solution to Buckley–Leverett Equation

Abstract

Efficient and economical hydrocarbon extraction relies on a clear understanding of fluid flow dynamics in subsurface reservoirs, where multiphase flow in porous media poses complex modeling challenges. Traditional numerical methods for solving the governing partial differential equations (PDEs) provide effective solutions but struggle with the high computational demands required for accurately capturing fine-scale flow dynamics. In response, this study introduces a physics-informed generative adversarial network (GAN) framework for addressing the Buckley–Leverett (B-L) equation with non-convex flux functions. The proposed framework consists of two novel configurations: a Physics-Informed Generator GAN (PIG-GAN) and Dual-Informed GAN (DI-GAN), both of which are rigorously tested in forward and inverse problem settings for the B-L equation. We assess model performance under noisy data conditions to evaluate robustness. Our results demonstrate that these GAN-based models effectively capture the B-L shock front, enhancing predictive accuracy while embedding fluid flow equations to ensure model interpretability. This approach offers a significant advancement in modeling complex subsurface environments, providing an efficient alternative to traditional methods in fluid dynamics applications.