针对物理模型预测偏差,提出可审计的分步修正框架。
ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models

- 分三阶段修正:全局纠偏、局部清洁、按风险分配算力。
- 在十个流态下,速度预测误差降低36倍以上,全局阶段纠错91%-99%。
- 无需微调模型,适合高可靠性科学计算场景。
偏微分方程(PDE)基础模型是预训练网络,能从单一通用求解器预测速度、压力等物理场演化。在陌生流动中,其预测会逐步漂移,误差集中在少数区域;重新训练会破坏模型稳定性,而统一后处理无法捕捉空间分布特性。为此,我们提出冻结求解器的后处理修正框架——自适应风险校准空间分诊与可审计优化(ARC-STAR)。该框架包含三个阶段:全局校正器消除整体求解器偏差,块级局部精修器清理全局残差,部署时无标签评分将有限算力路由至高风险块。框架具备三大特性:(i) 冻结宿主,不进行微调;(ii) 可审计,各阶段独立训练评估;(iii) 预算感知,通过块级接口实现全域修正或聚焦高风险区。在五个流动基准测试、覆盖十种流态条件下,ARC-STAR是唯一在每个流态上均使速度滚动误差比原始Poseidon模型降低至少36倍的方法。全局阶段降低原始主机误差91%-99%,局部阶段进一步减少剩余残差达94.4%。
原文摘要 · Abstract (English)
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%.
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