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Porous media processes involve various physical phenomena such as mechanicaldeformation, transport, and fluid flow. Accurate simulations must capture thestrong couplings between these phenomena. Choosing an efficient solver for themultiphysics problem usually entails the decoupling into subproblems related toseparate physical phenomena. Then, the suitable solvers for each subproblem andthe iteration scheme must be chosen. The wide range of options for the solvercomponents makes finding the optimum difficult and time-consuming; moreover,solvers come with numerical parameters that need to be optimized. As a furthercomplication, the solver performance may depend on the physical regime of thesimulation model, which may vary with time. Switching a solver with respect tothe dominant process can be beneficial, but the threshold of when to switchsolver is unclear and complicated to analyze. We address this challenge bydeveloping a machine learning framework that automatically searches for theoptimal solver for a given multiphysics simulation setup, based on statisticaldata from previously solved problems. For a series of problems, exemplified bysuccessive time steps in a time-dependent simulation, the framework updates andimproves its decision model online during the simulation. We show how itoutperforms preselected state-of-the-art solvers for test problem setups. Theexamples are based on simulations of poromechanics and simulations of flow andtransport. For the quasi-static linear Biot model, we demonstrate automatedtuning of numerical solver parameters by showing how the L-parameter of theso-called Fixed-Stress preconditioner can be optimized. Motivated by a testexample where the main heat transfer mechanism changes between convection anddiffusion, we discuss how the solver selector can dynamically switch solverswhen the dominant physical phenomenon changes with time.

Automated solver selection for simulation of multiphysics processes in porous media