Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training

Abstract

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.

References in corpus (17)

• On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks
• A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications
• Efficient training of physics-informed neural networks via importance sampling
• Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture
• Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics
• Solving the acoustic VTI wave equation using physics-informed neural networks
• Understanding and mitigating gradient pathologies in physics-informed neural networks
• Wavefield reconstruction inversion via physics-informed neural networks
• When and why PINNs fail to train: A neural tangent kernel perspective
• Learning Unknown Physics of non-Newtonian Fluids
• Physics-informed neural networks (PINNs) for fluid mechanics: A review
• Energy-based error bound of physics-informed neural network solutions in elasticity
• Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks
• NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework
• Physics Informed Deep Learning for Transport in Porous Media. Buckley Leverett Problem
• Physics-informed deep learning for flow and deformation in poroelastic media
• NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations

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