偏微分方程
人工神经网络
多孔介质
偏导数
流量(数学)
人工智能
物理
计算机科学
数学
数学分析
多孔性
机械
化学
有机化学
作者
Liqun Shan,Chengqian Liu,Yanchang Liu,Yazhou Tu,Liangliang Deng,Xiali Hei
出处
期刊:Advances in geo-energy research
[Yandy Scientific Press]
日期:2023-01-10
卷期号:8 (1): 37-44
被引量:3
标识
DOI:10.46690/ager.2023.04.04
摘要
Physical phenomenon in nature is generally simulated by partial differential equations. Among different sorts of partial differential equations, the problem of two-phase flow in porous media has been paid intense attention. As a promising direction, physics-informed neural networks shed new light on the solution of partial differential equations. However, current physics-informed neural networks’ ability to learn partial differential equations relies on adding artificial diffusion or using prior knowledge to increase the number of training points along the shock trajectory, or adaptive activation functions. To address these issues, this study proposes a physics-informed neural network with long short-term memory and attention mechanism, an ingenious method to solve the Buckley-Leverett partial differential equations representing two-phase flow in porous media. The designed network structure overcomes the dependency on artificial diffusion terms and enhances the importance of shallow features. The experimental results show that the proposed method is in good agreement with analytical solutions. Accurate approximations are shown even when encountering shock points in saturated fields of porous media. Furthermore, experiments show our innovative method outperforms existing traditional physics-informed machine learning approaches. Cited as: Shan, L., Liu, C., Liu, Y., Tu, Y., Dong, L., Hei, X. Physics-informed machine learning for solving partial differential equations in porous media. Advances in Geo-Energy Research, 2023, 8(1): 37-44. https://doi.org/10.46690/ager.2023.04.04
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