自适应网格加密的强化学习
Reinforcement Learning for Adaptive Mesh Refinement
摘要：
偏微分方程（PDE）控制的复杂物理系统的大规模有限元模拟关键取决于自适应网格加密（AMR）以将计算预算分配到需要更高分辨率的区域。现有的可扩展AMR方法基于瞬时误差估计做出启发式细化决策，因此不以整个模拟的长期最优性为目标。我们提出了一种新的AMR公式作为马尔可夫决策过程，并应用深度强化学习（RL）直接从模拟中训练细化策略。AMR提出了一个新的问题，RL的状态维度和可用的动作集的变化，在每一步，我们解决了提出新的政策架构具有不同的一般性和归纳偏见。这些策略架构的模型大小与网格大小无关，因此可以部署在比训练时使用的更大的模拟上。我们在静态函数估计和时间相关方程的综合实验中证明，RL策略可以在不使用地面实况解决方案的情况下对问题进行训练，与广泛使用的误差估计器竞争，并推广到更大，更复杂和看不见的测试问题。
英文摘要：
Large-scale finite element simulations of complex physical systems governed by partial differential equations (PDE) crucially depend on adaptive mesh refinement (AMR) to allocate computational budget to regions where higher resolution is required. Existing scalable AMR methods make heuristic refinement decisions based on instantaneous error estimation and thus do not aim for long-term optimality over an entire simulation. We propose a novel formulation of AMR as a Markov decision process and apply deep reinforcement learning (RL) to train refinement policies directly from simulation. AMR poses a new problem for RL as both the state dimension and available action set changes at every step, which we solve by proposing new policy architectures with differing generality and inductive bias. The model sizes of these policy architectures are independent of the mesh size and hence can be deployed on larger simulations than those used at train time. We demonstrate in comprehensive experiments on static function estimation and time-dependent equations that RL policies can be trained on problems without using ground truth solutions, are competitive with a widely-used error estimator, and generalize to larger, more complex, and unseen test problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
