Learning When to Refine: Long-Horizon Reinforcement Learning for Budgeted Neural-Operator PDE Solvers

The paper introduces a budgeted adaptive neural‑operator framework for solving time‑dependent PDEs, combining a global Fourier neural operator with a local patch‑wise residual corrector and a set‑aware selector that decides where to refine. A macro policy governs the timing and amount of refinement, and the authors propose rollout‑verified policy improvement (RV‑PI) to evaluate feasible refinement counts via actual rollouts, converting long‑horizon advantages into conservative policy targets and accepting updates only when held‑out trajectory error improves. Experiments on shallow‑water and Brusselator benchmarks show that RV‑PI outperforms immediate‑only and random macro policies, demonstrating that the value of a local correction depends on its downstream effect rather than just its immediate error reduction.

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• reinforcement-learning
• benchmarks