arXiv:2606.23215physics.data-ancs.AI2026-06

定位物理模型失效区域并识别缺失机制,给出可验证的统计证据。

Where Is My Physics Wrong? Localized and Identifiable Discovery of Model Discrepancy

  • 通过自动检测清洁区域,局部化误差至特定工况。
  • 在控制实验中将参数偏差降至0.002,定位F1提升至0.80。
  • 适合需要可信诊断的灰箱模型,如建筑能耗模拟。

混合模型结合可信物理规律与数据驱动修正,但物理模型通常仅在特定条件下失效。关键问题是:错误发生在哪里?缺失的机制是什么?证据是否具有统计显著性?现有稀疏发现和差异学习方法多采用全局修正,易将局部误差扩散至无误区域,扭曲物理参数,并缺乏校准的显著性判断。本文提出LISDD(局部可识别稀疏差异发现)框架,能将模型误差定位至特定运行区间,识别缺失机制的稀疏符号形式,并通过精确的小样本检验验证发现结果。LISDD首先在自动识别的清洁区间拟合已知物理模型,利用校准的残差能量统计量标记异常区域,通过候选库的全量留出法选择局部缺失项,并以样本分割F检验确认显著性。扩展的错误发现率控制可处理多个具有不同缺失机制的异常区域。在受控实验中,相比全局差异和黑箱基线,LISDD将物理参数偏差降至0.002(原为0.43),定位F1从0.44提升至0.80,以概率1恢复正确符号形式,实现精确检测,并在恢复所有预设机制的同时控制多区域错误发现率。该方法为物理定律在某一运行区间悄然失效的灰箱建筑能耗模型提供校准诊断工具。

原文摘要 · Abstract (English)

Hybrid models combine trusted physics with data-driven correction, but a physical model is rarely wrong everywhere or in the same way. The key diagnostic question is local: where does the model fail, what missing mechanism explains the failure, and is the evidence statistically real? Existing sparse-discovery and discrepancy-learning methods usually fit one global correction, which can spread a local error into clean regimes, bias trusted physical parameters, and provide no calibrated significance for selected terms. We introduce LISDD, Localized, Identifiable Sparse Discovery of Discrepancy, a framework that localizes model error to an operating regime, identifies a sparse symbolic form for the missing mechanism, and certifies the discovery with an exact finite-sample test. LISDD fits the known physics on an automatically detected clean regime, flags discrepant regions with a calibrated residual-energy statistic, selects the local missing term by exhaustive holdout over a candidate library, and confirms significance with a sample-split $F$-test. A false-discovery-rate extension handles multiple discrepant regions with different missing mechanisms. In controlled experiments, LISDD keeps physical-parameter bias at 0.002 versus 0.43 for global-discrepancy and black-box baselines, raises localization $F_1$ from 0.44 to 0.80, recovers the correct symbolic form with probability one, attains exact detection, and controls the multi-region false-discovery rate while recovering every planted mechanism. The result is a calibrated diagnostic tool for grey-box building-energy models when a fixed physical law silently breaks in one operating regime.

模型诊断物理信息稀疏发现统计验证

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