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

TL;DR

ARC-STAR is a novel post-hoc correction framework for PDE foundation models that improves accuracy, preserves pretrained networks, and enables budget-aware, region-specific refinements.

Contribution

It introduces a three-stage, frozen-solver correction method that is auditable and budget-aware, significantly reducing errors across multiple flow benchmarks.

Findings

Cuts velocity rollout error by at least 36x over raw Poseidon.

Reduces raw host error by 91-99% with the global stage.

Further reduces residuals by up to 94.4% with the local 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.