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 consists of decoupling into subproblems related to separate physical phenomena. Then, the suitable solvers for each subproblem and the outer iteration scheme must be chosen. The wide range of options for the solver components makes it difficult and time-consuming to find the optimum. To make matters more complicated, solvers come with numerical parameters that need to be optimized. Furthermore, different solvers perform best when different processes dominate in the model, for example, the transport process can switch between advection and diffusion dominance. Switching solvers with respect to the dominant process can be beneficial, but the boundaries of when to switch solvers are unclear and complicated to analyze. We have addressed 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, such as time steps in a time-dependent simulation, the framework updates and improves its decision model online during the simulation. We will 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 our test problem setups. Motivated by a test example where the main heat transfer mechanism changes between convection and diffusion, we will also discuss how the solver selector can dynamically switch solvers when the dominant physical phenomenon changes. Finally, we will talk about the cases when the automatic solver selection is beneficial and the limitations of its application.