Unknown Unknowns: Model Misspecification in Machine Learning for Physics

Juan Cruz-Martinez; Carolina Cuesta-Lazaro; Alexander Held; Michael Kagan

physics.data-anAug 13, 2026

Unknown Unknowns: Model Misspecification in Machine Learning for Physics

Authors: Juan Cruz-Martinez, Carolina Cuesta-Lazaro, Alexander Held, Michael Kagan

Organizations: Departamento de Física Atómica, Molecular y Nuclear, Universidad de Sevilla, E-41080 Sevilla, Spain · Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA · Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, USA · University of Wisconsin–Madison, 1205 University Ave, Madison, WI 53706, USA · SLAC National Accelerator Laboratory, 2575 Sand Hill Rd, Menlo Park, CA 94025, USA

Abstract

Machine learning is now a central tool for solving inverse problems in particle physics and astronomy. Models are trained on simulation and deployed on real data, raising the question not just of whether they fit, but of whether they are wrong in ways we did not anticipate: the unknown unknowns. This challenge of model misspecification is not unique to machine learning. In physics, misspecification is sometimes exactly what we want to find: new discoveries appear as failures of existing models. At other times, we want such effects absorbed into the analysis without biasing the measurement. A robust analysis is one that absorbs the misspecifications we are not interested in, while preserving sensitivity to the ones we are. Machine learning can both amplify misspecification and provide new tools to address it. We discuss the challenges of model misspecification, diagnostics for detecting it, and strategies for mitigation. No single diagnostic can confirm that a model is correctly specified: detection and mitigation are two halves of an iterative loop, in which a battery of complementary diagnostics is applied, the model is updated, and the process repeated. Robustness against unknown unknowns is ultimately less about any single technique than about a disposition: a willingness to suspect one's own model, and to design analyses that can survive being wrong in ways one did not anticipate.

Figures & tables

Panel of Figure 1 — Figure 1: Interpretations of possible scenarios of out-of-distribution (OOD) detectability and potential biases on inferred parameters due to model misspecification.

Metric	Advantages	Caveats
C2ST	Classifier to distinguish data from model samples, simple and broadly applicable.	No insight about hierarchy of different models.
OT	Cost of transforming between distributions. Offers a notion of geometric distance between models.	Very costly in high dimensions.
SW	Scalable alternative to the metric above, takes one-dimensional projections.	By projecting we might be missing important correlations or features.
MMD	Maps the sample to some kernel-defined feature space, bypassing the curse of dimensionality.	The choice of kernel acts as a bias.
$\chi^{2}$	Provides a straightforward metric for Gaussian-distributed histogrammed data.	Assumes statistically independent bins.
correlated $\chi^{2}$	Includes the covariance matrix in the calculation of the $\chi^{2}$ , bypassing its main weakness.	A reliable estimate of the covariance matrix is often very challenging (and even the source of misspecification).

Table 1: A bird’s-eye comparison of common goodness-of-fit metrics.

Panel of Figure 2 — Figure 2: Mitigation of model misspecification is an iterative process. Once issues are found, a mitigation strategy must be identified to result in an updated statistical model. The procedure repeats until no more problems can be found.

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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.

Abstract

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