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

2026-05-21

AI Summary

This work addresses the challenges of local error accumulation and stability degradation due to retraining in PDE foundation models when applied to unseen flow fields. To overcome these issues, the authors propose the ARC-STAR framework, which enables efficient and auditable post-hoc correction without fine-tuning the pre-trained solver. The approach employs a three-stage post-processing pipeline: global bias correction, block-wise local residual refinement, and unsupervised risk-score-driven adaptive refinement. This paradigm uniquely combines staged, tuning-free correction with high accuracy, stability, and computational controllability. Evaluated on five flow field benchmarks, ARC-STAR reduces roll-out velocity prediction errors by at least 36× compared to the original Poseidon model, eliminates 91–99% of errors in the global stage, and further suppresses residual errors by up to 94.4% in the local refinement stage.

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 https://anonymous.4open.science/r/arc_star.

Problem

• PDE foundation models
• post-hoc correction
• spatial error concentration
• auditable refinement
• compute budget

Innovation

• post-hoc correction
• PDE foundation models
• frozen-solver
• spatial triage
• auditable refinement