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（Dynamic Anticipatory Mesh Optimization），一种针对动态预测性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，传统自适应网格细化方法在处理时间依赖性问题时，通常仅依赖瞬时误差指标来指导自适应过程。因此，标准策略往往需要频繁重网格化以维持精度。在DynAMO方法中，多智能体强化学习被用于发现新的局部细化策略，这些策略能够预测并响应未来解的状态，生成可在更长时间区间内提供更精确解的网格。通过将DynAMO应用于二维线性对流方程和可压缩欧拉方程的间断伽辽金方法，我们证明这种新型网格细化范式能够超越传统基于阈值的策略，同时泛化至不同网格尺寸、重网格化与仿真时间以及初始条件。