Where Is My Physics Wrong? Localized and Identifiable Discovery of Model Discrepancy
2026-06-22 • Artificial Intelligence
Artificial Intelligence
AI summaryⓘ
The authors present LISDD, a new method for improving physical models by finding localized errors and missing parts in specific operating conditions. Unlike previous approaches that apply one correction everywhere, LISDD works by separating clean areas from problematic ones, identifying the exact missing mechanism in those regions, and statistically verifying the findings. Their experiments show that LISDD gives more accurate model parameters, better pinpoints where errors occur, and reliably discovers the true missing physics. This makes LISDD a useful tool for diagnosing and fixing models that work well in some cases but fail silently in others.
Hybrid modelsSparse discoveryModel discrepancyLocalized error detectionSymbolic regressionFinite-sample testFalse discovery rateGrey-box modelingResidual statisticsHoldout validation
Authors
Yifan Wang
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.