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

Researchers introduce LISDD, a framework for identifying where and why physics-based models fail by localizing errors to specific operating regimes and discovering sparse symbolic corrections. The method outperforms existing global-correction approaches by keeping parameter bias near zero while maintaining statistical rigor through finite-sample testing.

LISDD addresses a fundamental challenge in hybrid modeling: traditional discrepancy-learning methods apply corrections globally, inadvertently spreading localized errors across clean operating regimes and contaminating trusted physical parameters. This research reframes model diagnostics as a localization problem, recognizing that physical laws typically fail in specific contexts rather than uniformly.

The framework's innovation lies in its three-part methodology: automatically detecting clean regimes where known physics holds, flagging discrepant regions using calibrated residual statistics, and selecting missing terms through exhaustive holdout validation. The sample-split F-test provides certified significance without p-hacking, addressing a critical gap in existing sparse-discovery methods that often lack statistical calibration.

Experimental validation demonstrates substantial practical improvements. LISDD reduces physical-parameter bias from 0.43 to 0.002 compared to global baselines, improves localization accuracy (F1 from 0.44 to 0.80), and achieves exact detection while controlling false-discovery rates across multiple discrepant regions. These metrics matter for real-world applications like building-energy models, where silent failures in specific operating conditions (e.g., extreme temperatures) can accumulate substantial errors before detection.

For the scientific computing and machine-learning communities, LISDD establishes a template for interpretable hybrid modeling that maintains physical credibility. The approach scales to grey-box systems where complete mechanistic understanding remains elusive but partial knowledge exists. Future applications likely extend to climate modeling, materials science, and engineering systems where physics provides foundational constraints but empirical corrections remain necessary.

• →LISDD localizes model failures to specific operating regimes rather than applying global corrections that contaminate clean data regions
• →The framework recovers correct symbolic forms with probability one while maintaining parameter bias near zero, outperforming existing baselines by 200x
• →Finite-sample F-testing provides calibrated statistical significance, eliminating arbitrary term selection in sparse discovery
• →Multi-region false-discovery-rate control enables detection of multiple distinct missing mechanisms within single models
• →Method targets grey-box systems where partial physics knowledge exists but empirical corrections remain necessary