Physics-informed machine learning for solving partial differential equations in porous media

Physical phenomenon in nature is generally simulated by partial differential equations. Among different sorts of equations, the problem two-phase flow porous media has been paid intense attention. As a promising direction, physics-informed neural networks shed new light on solution However, current networks’ ability to learn equations relies adding artificial diffusion or using prior knowledge increase number training points along shock trajectory, adaptive activation functions. To address these issues, this study proposes network with long short-term memory and attention mechanism, an ingenious method solve Buckley-Leverett representing media. The designed structure overcomes dependency terms enhances importance shallow features. experimental results show that proposed good agreement analytical solutions. Accurate approximations are shown even when encountering saturated fields Furthermore, experiments our innovative outperforms existing traditional machine learning approaches. Cited as: Shan, L., Liu, C., Y., Tu, Dong, Hei, X. Physics-informed for solving Advances Geo-Energy Research, 2023, 8(1): 37-44. https://doi.org/10.46690/ager.2023.04.04