A physics-informed neural network is presented for poroelastic problems with coupled flow and deformation processes. The governing equilibrium and mass balance equations are discussed and specific derivations for two-dimensional cases are presented. A fully-connected deep neural network is used for training. Barry and Mercer's source problem with time-dependent fluid injection/extraction in an idealized poroelastic medium, which has an exact analytical solution, is used as a numerical example. A random sample from the analytical solution is used as training data and the performance of the model is tested by predicting the solution on the entire domain after training. The deep learning model predicts the horizontal and vertical deformations well while the error in the predicted pore pressure predictions is slightly higher because of the sparsity of the pore pressure values.

中文翻译：

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多孔弹性介质中流动和变形的基于物理的深度学习

针对具有耦合流动和变形过程的多孔弹性问题，提出了一种基于物理的神经网络。讨论了控制平衡和质量平衡方程，并提出了二维情况的具体推导。一个全连接的深度神经网络用于训练。Barry 和 Mercer 的源问题在理想化多孔弹性介质中具有时间相关的流体注入/提取，具有精确的解析解，用作数值示例。将解析解中的随机样本作为训练数据，通过在训练后在整个域上预测解来测试模型的性能。