Physics-informed neural networks (PINNs) have received significant attention as a unified framework for forward, inverse, and surrogate modeling of problems governed by partial differential equations (PDEs). Training PINNs for forward problems, however, pose significant challenges, mainly because of the complex non-convex and multi-objective loss function. In this work, we present a PINN approach to solving the equations of coupled flow and deformation in porous media for both single-phase and multiphase flow. To this end, we construct the solution space using multi-layer neural networks. Due to the dynamics of the problem, we find that incorporating multiple differential relations into the loss function results in an unstable optimization problem, meaning that sometimes it converges to the trivial null solution, other times it moves very far from the expected solution. We report a dimensionless form of the coupled governing equations that we find most favourable to the optimizer. Additionally, we propose a sequential training approach based on the stress-split algorithms of poromechanics. Notably, we find that sequential training based on stress-split performs well for different problems, while the classical strain-split algorithm shows an unstable behaviour similar to what is reported in the context of finite element solvers. We use the approach to solve benchmark problems of poroelasticity, including Mandel's consolidation problem, Barry-Mercer's injection-production problem, and a reference two-phase drainage problem. The Python-SciANN codes reproducing the results reported in this manuscript will be made publicly available at https://github.com/sciann/sciann-applications.
翻译:物理知情的神经网络(PINNs)作为前方、反面和代谢模拟部分差异方程式(PDEs)问题的统一框架,受到极大关注。然而,对前方问题的培训PINNs提出了重大挑战,这主要是因为复杂的非康维克斯和多目标损失功能。在这项工作中,我们提出了一个PINN 方法,以解决单阶段和多阶段流动的多功能媒体中混合流和变形的方程式的方程式。为此,我们利用多层神经网络构建了解决方案空间。由于问题的动态,我们发现将多种差异关系纳入损失函数导致一个不稳定的优化问题,这意味着有时它会与微不足道的零解决方案相融合,有时它会远离预期的解决方案。我们报告的是一种无维的组合式方程式,我们发现一种基于压力-平衡算法的顺序培训方法。我们发现,基于压力-螺旋型螺旋型螺旋型螺旋型计算法的连续进行培训,我们发现基于压力-螺旋型螺旋型代码的参考方法,我们发现, 将一个稳定的硬性内基质的内基质- 质- 质- 质- 质- 递化- 质- 度- 质- 质- 质- 质- 度- 度- 度- 度- 度- 递解- 度- 质性- 度- 度- 度- 度- 度- 度- 度- 度- 度- 质- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度- 度-