We introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost and solution accuracy in numerical methods for partial differential equations. However, traditional adaptive mesh refinement approaches for time-dependent problems typically rely only on instantaneous error indicators to guide adaptivity. As a result, standard strategies often require frequent remeshing to maintain accuracy. In the DynAMO approach, multi-agent reinforcement learning is used to discover new local refinement policies that can anticipate and respond to future solution states by producing meshes that deliver more accurate solutions for longer time intervals. By applying DynAMO to discontinuous Galerkin methods for the linear advection and compressible Euler equations in two dimensions, we demonstrate that this new mesh refinement paradigm can outperform conventional threshold-based strategies while also generalizing to different mesh sizes, remeshing and simulation times, and initial conditions.

翻译：我们提出DynAMO——一种面向动态预测网格优化的强化学习范式。自适应网格细化是偏微分方程数值方法中优化计算成本与求解精度的有效工具。然而，传统的自适应网格细化方法在处理时间相关问题时常仅依赖瞬时误差指标指导自适应过程，导致标准策略需频繁重划网格以保持精度。DynAMO方法利用多智能体强化学习发现新的局部细化策略，该策略能够预测并响应未来解状态，通过生成可在更长时间区间内提供更高精度解的网格。将DynAMO应用于二维线性平流与可压缩欧拉方程的不连续伽辽金方法时，我们验证了这种新型网格细化范式不仅能超越传统阈值策略的表现，还能推广至不同网格尺寸、重划网格与模拟时长以及初始条件。