Reinforcement Learning-Based Adaptive Mesh Refinement Method for Plasma Diffusion Evolution
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摘要: 通过在电离层空间释放等离子体,模拟等离子体在电离层中的扩散演化特征是研究电离层物理机制的一种重要手段。然而,等离子体在电离层中的扩散演化动力学属于高度复杂非线性多尺度问题,对其进行精确数值模拟对计算效率要求极高。传统的自适应网格剖分技术是解决计算精度及效率的重要方法,但其高度依赖人工设计的误差指示器,在处理复杂非线性问题时泛化性不足。本文研究基于强化学习的网格剖分方法,将网格剖分重构为一个马尔可夫决策过程,把静态网格优化转化为序列决策任务,通过构建基于图结构的网格特征表示,利用图注意力机制深度编码邻域物理信息,引入多智能体强化学习框架,可实现多网格单元的协同细化决策。以二维对流方程为例进行仿真实验,结果表明,与传统自适应网格剖分方法相比,计算效率提升约 6%~11%。此外,该策略在降低网格更新频率的情况下仍能维持优异的误差控制能力,展现出强健的数值稳定性与环境适应性。Abstract: 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.
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