Abstract: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%. Our code implementation is available at this https URL.
| Comments: | 40 pages, including appendices |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.22222 [cs.LG] |
| (or arXiv:2605.22222v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.22222 arXiv-issued DOI via DataCite (pending registration) |
From: Chengze Li [view email]
[v1]
Thu, 21 May 2026 09:26:16 UTC (1,185 KB)
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