# ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models

arXiv: https://arxiv.org/abs/2605.22222 · HTML: https://mlsanity.com/paper/2605.22222/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 64 references that are in the map.
- First posted on arXiv 21 May 2026.

## Builds on (most cited first, 30 of 43)

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## Abstract (arXiv)

Partial differential equation (PDE) foundation models are pretrained networks that forecast how physical fields like velocity and pressure evolve from a single reusable solver. On unfamiliar flows their predictions drift step by step, errors concentrate in a few regions, yet retraining destabilizes the network and uniform post-hoc correction overlooks this spatial concentration. To address this, we propose a frozen-solver post-hoc correction framework, Adaptive Risk-Calibrated Spatial Triage for Auditable Refinement (ARC-STAR). ARC-STAR organizes correction into three stages: a global corrector removes broad solver bias, a blockwise local refiner cleans the post-global residual, and, at deployment, a label-free score routes refinement to high-risk blocks under a compute budget. The framework is designed to be (i) frozen-host, preserving the pretrained solver without fine-tuning; (ii) auditable, with global and local stages trained and evaluated separately for measurable contributions; and (iii) budget-aware, using a blockwise interface that either refines the full field or routes limited compute to high-risk regions. Across five flow benchmarks spanning ten regime cells, ARC-STAR is the only method that cuts velocity rollout error by at least 36x over raw Poseidon on every cell. The global stage reduces raw host error by 91-99%, and the local stage further reduces the remaining post-global residual by up to 94.4%.