Reinforcement Learning for the Optimization of Explicit Runge-Kutta Method Parameters

Abstract: Reinforcement learning is one of the three main paradigms in machine learning, which is increasingly used as a method to approach scientific problems. In this thesis, we introduce and use reinforcement learning to find the optimal parameters of a numerical solver. We first motivate that solving the linear systems can be done by solving initial value problems. These initial values problems can then be solved with an explicit, two stages Runge-Kutta solver, for which we need to find the optimal parameters for the solver, depending on the parameters of the problem. Using reinforcement learning, and in particular policy gradient methods, we find that with some care, reinforcement learning can be used to learn the solver parameters as a function of the problem parameters. These results are however tempered by some limitations, as the solver can diverge in certain cases, and convergence speed remains low in general.