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

• URL: http://arxiv.org/abs/2606.23215v1
• Date: Mon, 22 Jun 2026 12:03:14 GMT
• Title: Where Is My Physics Wrong? Localized and Identifiable Discovery of Model Discrepancy
• Abstract summary: We introduce LISDD, Localized, Identifiable Sparse Discovery of Discrepancy, a framework that localizes model error to an operating regime.<n>A false-discovery-rate extension handles multiple discrepant regions with different missing mechanisms.<n>The result is a calibrated diagnostic tool for grey-box building-energy models when a fixed physical law silently breaks in one operating regime.
• Score: 6.016090674751934
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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