Unknown Unknowns: Model Misspecification in Machine Learning for Physics

In High Energy Physics, as in many other fields of science, the application of machine learning techniques has been crucial in advancing our understanding of fundamental phenomena. Increasingly, deep learning models are applied to analyze both simulated and experimental data. In most experiments, a rigorous regime of testing for physically motivated systematic uncertainties is in place. The numerical evaluation of these tests for differences between the data on the one side and simulations on the other side quantifies the effect of potential sources of mismodelling on the machine learning output. In addition, thorough comparisons of marginal distributions and (linear) feature correlations between data and simulation in "control regions" are applied. However, the guidance by physical motivation, and the need to constrain comparisons to specific regions, does not guarantee that all possible sources of deviations have been accounted for. We therefore propose a new adversarial attack - the CONSERVAttack - designed to exploit the remaining space of hypothetical deviations between simulation and data after the above mentioned tests. The resulting adversarial perturbations are consistent within the uncertainty bounds - evading standard validation checks - while successfully fooling the underlying model. We further propose strategies to mitigate such vulnerabilities and argue that robustness to adversarial effects must be considered when interpreting results from deep learning in particle physics.

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.

We review the concepts of interpretability and explainability as they apply to machine learning in physics. We define interpretability as concerning the structural transparency of a model (the ability to understand or approximate its inner workings) and explainability as concerning the scientific content of a model (the ability to map it onto domain knowledge). We discuss the trade-offs each entails (interpretability vs. expressivity; explainability vs. adaptability), the contexts in which each is needed, and the intrinsic and post-hoc tools available for achieving them. Throughout, we emphasize that machine-learned models are subject to the same scientific questions as classical models, differing only in scale, and that interpretability and explainability are best understood as deliberate modeling choices rather than inherent properties. We also emphasize the importance of task specification and intervention plans as a core aspect of model design.