Porous media processes involve various physical phenomena such as mechanical deformation, transport, and fluid flow. Accurate simulations must capture the strong couplings between these phenomena. Choosing an efficient solver for a multiphysics problem usually entails the decoupling into subproblems related to separate physical phenomena. Then, the suitable solvers for each subproblem and the iteration scheme must be chosen. Finally, the numerical parameters of the solvers must be optimized. Theoretical considerations often allow us to come up with several robust linear solvers for a given problem, but they cannot guide us further in seeking the most efficient linear solver configuration because its performance depends on hardware, software and the driving forces of the simulated model. As a further complication, these driving forces can vary with time within one simulation, causing the most efficient linear solver configuration to change. Switching a solver with respect to the dominant process can be beneficial, but the threshold of when to switch solver is unclear and complicated to analyze. We address this challenge by developing a machine learning framework that automatically searches for the optimal solver for a given multiphysics simulation setup, based on statistical data from previously solved problems. For a series of problems, exemplified by successive time steps in a time-dependent simulation, the framework updates and improves its decision model online during the simulation. We describe the solver selection algorithm, present examples of how the solver selector tunes the solver during the simulation, and show how it outperforms preselected state-of-the-art solvers for test problem setups. The examples are based on simulations of poromechanics and simulations of flow and transport. For the quasi-static linear Biot model, we demonstrate automated tuning of numerical solver parameters by showing how the L-parameter of the so-called Fixed-Stress preconditioner can be optimized. Motivated by a test example where the main heat transfer mechanism changes between convection and diffusion, we also discuss how the solver selector can dynamically switch solvers when the dominant physical phenomenon changes with time.

中文翻译：

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用于模拟多孔介质中多物理场过程的自动线性求解器选择


多孔介质过程涉及各种物理现象，例如机械变形、传输和流体流动。准确的模拟必须捕捉这些现象之间的强耦合。为多物理场问题选择有效的求解器通常需要解耦为与单独的物理现象相关的子问题。然后，必须为每个子问题选择合适的求解器和迭代方案。最后，必须优化求解器的数值参数。理论考虑通常使我们能够针对给定问题提出几个鲁棒的线性求解器，但它们无法指导我们进一步寻求最有效的线性求解器配置，因为其性能取决于硬件、软件和仿真模型的驱动力。更复杂的是，这些驱动力可能会在一次模拟中随时间变化，从而导致最有效的线性求解器配置发生变化。相对于主导过程切换求解器可能是有益的，但何时切换求解器的阈值尚不清楚且分析起来很复杂。我们通过开发一个机器学习框架来应对这一挑战，该框架根据先前解决的问题的统计数据自动搜索给定多物理场仿真设置的最佳求解器。对于一系列问题，例如依赖时间的模拟中的连续时间步，该框架在模拟过程中在线更新和改进其决策模型。我们描述了求解器选择算法，提供了求解器选择器如何在仿真过程中调整求解器的示例，并展示了它如何优于测试问题设置中预先选择的最先进的求解器。 这些示例基于孔隙力学模拟以及流动和传输模拟。对于准静态线性 Biot 模型，我们通过展示如何优化所谓的固定应力预处理器的 L 参数来演示数值求解器参数的自动调整。受主要传热机制在对流和扩散之间变化的测试示例的启发，我们还讨论了当主要物理现象随时间变化时，求解器选择器如何动态切换求解器。