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 the 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. The wide range of options for the solver components makes finding the optimum difficult and time-consuming; moreover, solvers come with numerical parameters that need to be optimized. As a further complication, the solver performance may depend on the physical regime of the simulation model, which may vary with time. 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 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 discuss how the solver selector can dynamically switch solvers when the dominant physical phenomenon changes with time.

翻译：孔隙介质过程涉及力学变形、输运及流体流动等多种物理现象。精确模拟必须捕捉这些现象间的强耦合关系。针对多物理问题选择高效求解器通常需要将其解耦为与各物理现象相关的子问题，进而为每个子问题选择合适求解器并确定迭代方案。求解器组件的广泛选择使得最优配置的发现变得困难且耗时；此外，求解器自身包含需优化的数值参数。更复杂的是，求解器性能可能随模拟模型物理状态的变化而改变，且该状态具有时变特性。根据主导过程切换求解器可能带来优势，但切换阈值的界定尚不明确且分析困难。我们通过开发机器学习框架应对这一挑战——该框架基于历史求解问题的统计数据，自动为给定多物理模拟配置搜索最优求解器。以时变模拟中连续时间步为例，框架在模拟过程中在线更新并改进决策模型。研究表明，该框架在测试问题配置上优于预先选定的最优求解器。实例基于孔隙力学模拟及流动-输运模拟展开。针对准静态线性比奥模型，我们演示了如何通过优化固定应力预条件子的L参数实现数值求解器参数的自动调节。基于传热机制在对流与扩散间切换的测试案例，我们探讨了求解器选择器如何随主导物理现象的时间演变动态切换求解器。