---
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id: "4000ede4eb801587211df327fc76257869371958b907b00ebabff53b957e8dce"
canonical_url: "https://aidr.today/4000ede4?lang=en"
title: "Learning When to Refine: Long-Horizon Reinforcement Learning for Budgeted Neural-Operator PDE Solvers"
lang: "en"
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available_langs: ["en","vi"]
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published_at: "2026-10-07T04:00:00.000Z"
category: "Research"
topics: ["inference"]
source_urls: ["https://arxiv.org/abs/2610.06883"]
summary: "A budgeted adaptive neural-operator solver uses a global Fourier neural operator, a local patch-wise correction operator, and a set-aware selector guided by a macro policy to allocate a finite refinement budget over time. Rollout-verified policy improvement (RV-PI) evaluates feasible refinement counts through continuation rollouts and accepts updates only when held-out trajectory error improves, achieving a three-seed mean trajectory relative L2 error of 0.6910 on the shallow-water benchmark with a 32-intervention budget."
---

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

> [Open the canonical story](<https://aidr.today/4000ede4?lang=en>)

**Published:** 2026-10-07T04:00:00.000Z
**Category:** Research
**Topics:** inference

## Summary

A budgeted adaptive neural\-operator solver uses a global Fourier neural operator, a local patch\-wise correction operator, and a set\-aware selector guided by a macro policy to allocate a finite refinement budget over time\. Rollout\-verified policy improvement \(RV\-PI\) evaluates feasible refinement counts through continuation rollouts and accepts updates only when held\-out trajectory error improves, achieving a three\-seed mean trajectory relative L2 error of 0\.6910 on the shallow\-water benchmark with a 32\-intervention budget\.

## Sources

- [Story source](<https://arxiv.org/abs/2610.06883>)