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.

Computer tomography technology is widely used in geological exploration because it is a nondestructive and three-dimensional imaging method that can be integrated with computer simulation. However, the large-scale application of the computer tomography technique is limited by economic costs and time consumption. Therefore, it is challenging and intractable to indicate the pore structure characteristics of rock. To address this issue, a super-resolution reconstruction algorithm based on convolutional neural networks, residual learning, and attention mechanism was proposed to generate super-resolution images in this study. This algorithm was applied to the reconstruction of carbonate rock and sandstone. The performance of two-dimensional image reconstruction was evaluated by quantitative extraction and qualitative visualization. The results from experiments indicate that the built model performs well on different upscaling factors and is superior to the existing super-resolution approaches based on convolutional neural network.