Adaptive Mesh Refinement (AMR) is crucial for mesh-based simulations, as it
allows for dynamically adjusting the resolution of a mesh to trade off
computational cost with the simulation accuracy. Yet, existing methods for AMR
either use task-dependent heuristics, expensive error estimators, or do not
scale well to larger meshes or more complex problems. In this paper, we
formalize AMR as a Swarm Reinforcement Learning problem, viewing each element
of a mesh as part of a collaborative system of simple and homogeneous agents.
We combine this problem formulation with a novel agent-wise reward function and
Graph Neural Networks, allowing us to learn reliable and scalable refinement
strategies on arbitrary systems of equations. We experimentally demonstrate the
effectiveness of our approach in improving the accuracy and efficiency of
complex simulations. Our results show that we outperform learned baselines and
achieve a refinement quality that is on par with a traditional error-based AMR
refinement strategy without requiring error indicators during inference.

使用 Swarm 强化学习及 Graph 神经网络，将自适应网格细化问题形式化为协作系统，优于传统基于误差的方法，可在复杂模拟中提高准确性和效率。