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Beyond constant error: Heteroscedastic Bayesian model combination for modeling unmeasured nuclei

B. Knight1,2,*, S. Lalit1,†, P. Giuliani1,‡, K. Godbey1,§, W. Nazarewicz1,2,∥, A. Ravlić1,3,¶, and P.-G. Reinhard4,**

  • *Contact author: knight@frib.msu.edu
  • †Contact author: lalit@frib.msu.edu
  • ‡Contact author: giulianp@frib.msu.edu
  • §Contact author: me@kyle.ee
  • ∥Contact author: witek@frib.msu.edu
  • Contact author: ravlic@frib.msu.edu
  • **Contact author: paul-gerhard.reinhard@fau.de
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Phys. Rev. Research 8, 043130 – Published 4 November, 2026

DOI: https://doi.org/10.1103/z7g9-7d74

Abstract

Experimentally inaccessible regions of the nuclear chart remain a challenge for global models of atomic nuclei to predict. This includes exotic nuclei near particle drip lines, superheavy elements at the extremes of mass and charge, and the neutron-rich pathways of astrophysical processes in explosive stellar environments where heavy elements are created. Given that individual nuclear models are imperfect, deep extrapolations are best approached using model ensembles, which allow for the systematic combination of diverse theoretical predictions. In this study, we employ the recently introduced Bayesian model combination (BMC) method, based on statistical machine learning, that provides robust uncertainty quantification for forecasts using model ensembles. To account for the inherent degradation of predictive power as models extrapolate into the yet-unexplored domain, we introduce a heteroscedastic BMC framework in which the combined theoretical uncertainty is treated as a dynamic quantity. We apply this methodology to an ensemble of realistic energy density functionals with a specific focus on the Z=46–52 isotopic chains. We rigorously validate the approach using both experimental data and synthetic data designed to assess performance in the deep extrapolation regime. Our results demonstrate that the proposed heteroscedastic approach yields superior calibration metrics and provides statistically principled assessments of the particle drip lines.

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Phys. Rev. Research 8, 043130– Published 4 November, 2026
  • Received 15 July 2026
  • Accepted 19 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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