  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.
