  We explore a reinforcement learning strategy to automate and accelerate
h/p-multigrid methods in high-order solvers. Multigrid methods are very
efficient but require fine-tuning of numerical parameters, such as the number
of smoothing sweeps per level and the correction fraction (i.e., proportion of
the corrected solution that is transferred from a coarser grid to a finer
grid). The objective of this paper is to use a proximal policy optimization
algorithm to automatically tune the multigrid parameters and, by doing so,
improve stability and efficiency of the h/p-multigrid strategy.
  Our findings reveal that the proposed reinforcement learning h/p-multigrid
approach significantly accelerates and improves the robustness of steady-state
simulations for one dimensional advection-diffusion and nonlinear Burgers'
equations, when discretized using high-order h/p methods, on uniform and
nonuniform grids.
