论文标题
物理信息为毛弹性介质中的流量和变形而深入学习
Physics-informed deep learning for flow and deformation in poroelastic media
论文作者
论文摘要
出现了有关耦合流和变形过程的毛弹性问题的物理信息神经网络。讨论了管理平衡和质量平衡方程，并提出了二维病例的特定推导。完全连接的深神经网络用于培训。 Barry和Mercer在具有时间依赖性的流体注入/提取的源源问题（具有精确的分析溶液）被用作数值示例。分析解决方案中的随机样品用作训练数据，并通过预测训练后整个域上的解决方案来测试模型的性能。深度学习模型可以很好地预测水平和垂直变形，而预测的孔隙压力预测中的误差则略高，因为孔隙压力值的稀疏性。
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.
