A reinforcement learning strategy for p-adaptation in high order solvers
David Huergo Gonzalo Rubio Esteban Ferrer
Reinforcement learning (RL) has emerged as a promising approach to automating
decision processes. This paper explores the application of RL techniques to
optimise the polynomial order in the computational mesh when using high-order
solvers. Mesh adaptation plays a crucial role in improving the efficiency of
numerical simulations by improving accuracy while reducing the cost. Here,
actor-critic RL models based on Proximal Policy Optimization offer a
data-driven approach for agents to learn optimal mesh modifications based on
evolving conditions.
  The paper provides a strategy for p-adaptation in high-order solvers and
includes insights into the main aspects of RL-based mesh adaptation, including
the formulation of appropriate reward structures and the interaction between
the RL agent and the simulation environment. We discuss the impact of RL-based
mesh p-adaptation on computational efficiency and accuracy. We test the RL
p-adaptation strategy on a 1D inviscid Burgers' equation to demonstrate the
effectiveness of the strategy. The RL strategy reduces the computational cost
and improves accuracy over uniform adaptation, while minimising human
intervention.