arXiv：cs.LG· Ange Tong·· 4 小时前AI 评分35
学习何时精修：面向预算受限神经算子 PDE 求解器的长时程强化学习
Learning When to Refine: Long-Horizon Reinforcement Learning for Budgeted Neural-Operator PDE Solvers
AI 导读
研究提出"预算受限自适应神经算子求解"框架：全局 Fourier 神经算子推进整个场，局部算子提出分块残差修正，由集合感知选择器决定修正位置，宏观策略决定何时及花多少剩余修正预算。
正文
Abstract:Neural operators provide fast surrogates for time-dependent PDEs, but autoregressive deployment creates a refinement-allocation problem: prediction errors vary over space and time, while only a finite number of local corrections can be committed along a trajectory. We formulate this as budgeted adaptive neural-operator solving. A global Fourier neural operator advances the full field, a local operator proposes patch-wise residual corrections, and a set-aware selector chooses where to refine. A macro policy decides when and how much of the remaining refinement budget to spend. We introduce rollout-verified policy improvement (RV-PI), which evaluates feasible refinement counts through actual continuation rollouts of the learned PDE solver, converts long-horizon advantages into conservative policy targets, and accepts an update only when held-out trajectory error improves. On the shallow-water benchmark with a 32-intervention budget, RV-PI achieves a three-seed mean trajectory relative L2 error of 0.6910, improving over immediate-only policy improvement by 5.37% and RandomMacro by 2.41%. On the forcing-driven Brusselator benchmark with a 76-intervention budget, RV-PI attains 0.09954, improving over immediate-only policy improvement by 2.31% and RandomMacro by 5.32%. These results show that, under a fixed refinement budget, the value of a local correction depends on its downstream effect on the autoregressive trajectory, not only on its immediate error reduction.
| Comments: | 21 pages, 4 figures, 2 tables |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.06883 [cs.LG] |
| (or arXiv:2610.06883v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.06883 arXiv-issued DOI via DataCite |
Submission history
From: Ange Tong [view email]
[v1]
Sat, 19 Sep 2026 12:17:32 UTC (2,400 KB)
来源：arXiv：cs.LG · arxiv.org