论文标题
在多孔介质中的热杂种机械（THM）过程的物理信息神经网络解决方案
Physics-informed neural network solution of thermo-hydro-mechanical (THM) processes in porous media
论文作者
论文摘要
物理知识的神经网络（PINN）已获得对偏差方程（PDE）描述的问题的远期，反和替代建模的兴趣。但是，它们在多个物理问题上的应用，受几个耦合PDE的约束，提出了独特的挑战，这些挑战阻碍了这种方法的鲁棒性和广泛适用性。在这里，我们研究了PINN在多孔培养基中涉及热 - 氢机械（THM）过程的问题的正向解中的应用，这些介质在热导率，水力渗透性和弹性中表现出不同的空间和时间尺度。此外，Pinn面临优化问题的多目标和非凸性性质的挑战。为了解决这些基本问题，我们：（1）〜以无量纲形式重写，最适合深入学习算法的方程式； （2）〜提出了一种顺序训练策略，该策略规避了对多物理问题的同时解决方案的需求，并促进了解决方案搜索中优化器的任务； （3）〜利用自适应重量策略来克服多目标优化问题的梯度流中的刚度。最后，我们将此框架应用于1D和〜2d中几个合成问题的解决方案。
Physics-Informed Neural Networks (PINNs) have received increased interest for forward, inverse, and surrogate modeling of problems described by partial differential equations (PDE). However, their application to multiphysics problem, governed by several coupled PDEs, present unique challenges that have hindered the robustness and widespread applicability of this approach. Here we investigate the application of PINNs to the forward solution of problems involving thermo-hydro-mechanical (THM) processes in porous media, which exhibit disparate spatial and temporal scales in thermal conductivity, hydraulic permeability, and elasticity. In addition, PINNs are faced with the challenges of the multi-objective and non-convex nature of the optimization problem. To address these fundamental issues, we: (1)~rewrite the THM governing equations in dimensionless form that is best suited for deep-learning algorithms; (2)~propose a sequential training strategy that circumvents the need for a simultaneous solution of the multiphysics problem and facilitates the task of optimizers in the solution search; and (3)~leverage adaptive weight strategies to overcome the stiffness in the gradient flow of the multi-objective optimization problem. Finally, we apply this framework to the solution of several synthetic problems in 1D and~2D.
