Reinforcement Learning-Based Adaptive Mesh Refinement Method for Plasma Diffusion Evolution

Simulating the diffusion and evolution of plasma in the ionosphere by releasing plasma into ionospheric space is an important method for studying the physical mechanisms of the ionosphere. However, the dynamics of plasma diffusion and evolution in the ionosphere constitute a highly complex, nonlinear, multiscale problem, and performing accurate numerical simulations of it demands extremely high computational efficiency. Traditional adaptive mesh refinement (AMR) techniques are key methods for addressing computational accuracy and efficiency, but they rely heavily on manually designed error metrics and lack sufficient generalizability when dealing with complex nonlinear problems. This paper investigates a reinforcement learning-based mesh refinement method that reformulates mesh refinement as a Markov decision process, transforming static mesh optimization into a sequential decision-making task. By constructing a graph-based representation of mesh features and utilizing a graph attention mechanism to deeply encode local physical information, a multi-agent reinforcement learning framework is introduced to enable collaborative refinement decisions across multiple mesh elements. Simulation experiments using the two-dimensional convection equation demonstrate that, compared to traditional adaptive mesh refinement methods, computational efficiency is improved by approximately 6% to 11%. Furthermore, this strategy maintains excellent error control capabilities even at reduced mesh update frequencies, exhibiting robust numerical stability and environmental adaptability.