- Physical Review Journals
All JournalsPhysics Magazine

APS Open Science

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Physics-guided ensemble learning of nuclear masses for astrophysical applications

Srikrishna Agrawal*

N. Chandnani

T. Ghosh and N. Paar

G. Saxena†

B. K. Agrawal

  • Department of Physics, Manipal University Jaipur, Jaipur 303007, India and Department of Physics (H&S), Government Women Engineering College, Ajmer 305002, India

  • Department of Physics, Faculty of Science, University of Zagreb, Bijenička cesta 32, Zagreb 10000, Croatia

  • Department of Physics (H&S), Government Women Engineering College, Ajmer 305002, India

  • *Contact author: agrawalsrikrishna0411@gmail.com
  • †Contact author: gauravphy@gmail.com
PDF

APS Open Sci. 1, 000085 – Published 6 August, 2026

DOI: https://doi.org/10.1103/8n1w-f3b7

Abstract

The gradient boosting regressor, an ensemble learning technique, is utilized to correct the residuals in nuclear mass excess across six different nuclear mass models. The corrected residuals are substantially reduced and further improved by applying a weighted averaging method, which benefits from partial error cancellation among the models. Our proposed conflated model, combining ensemble learning with model averaging (ELMA), achieves a root mean square error (RMSE) of approximately 57 keV, well below the critical threshold of 100 keV, for the full dataset of the Atomic Mass Evaluation (AME2020). ELMA also improves predictions for nuclei beyond the training region, with the weighted ensemble reducing the RMSE by approximately 25%–45% relative to the best individual mass model on independent extrapolative datasets. The reliability of the ELMA approach is further validated through the calculation of α-decay Q values, where a clear reduction in deviations from experimental data is observed compared to individual nuclear mass model predictions. We have also compiled a mass excess and binding energy of 6300 nuclei, obtained using our framework and serves as a valuable resource for nuclear physics research and is publicly available through the ELMA web interface (https://ddnp.in/).

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (49)

  1. D. Martin, A. Arcones, W. Nazarewicz, and E. Olsen, Impact of nuclear mass uncertainties on the r process, Phys. Rev. Lett. 116, 121101 (2016).
  2. M. Arnould, S. Goriely, and K. Takahashi, The r-process of stellar nucleosynthesis: Astrophysics and nuclear physics achievements and mysteries, Phys. Rep. 450, 97 (2007).
  3. D. Lunney and I. Collaboration, Extending and refining the nuclear mass surface with ISOLTRAP, J. Phys. G: Nucl. Part. Phys. 44, 064008 (2017).
  4. M. Smith, M. Brodeur, T. Brunner, S. Ettenauer, A. Lapierre, R. Ringle, V. L. Ryjkov, F. Ames, P. Bricault, G. W. F. Drake, P. Delheij, D. Lunney, F. Sarazin, and J. Dilling, First Penning-trap mass measurement of the exotic halo nucleus Li11, Phys. Rev. Lett. 101, 202501 (2008).
  5. M. Hausmann et al., Isochronous mass measurements of hot exotic nuclei, Hyperfine Interact. 132, 289 (2001).
  6. T. Yamaguchi, Y. Yamaguchi, and A. Ozawa, The challenge of precision mass measurements of short-lived exotic nuclei: Development of a new storage ring mass spectrometry, Int. J. Mass Spectrom. 349–350, 240 (2013).
  7. A. Czihaly, S. Beck, J. Bergmann, C. L. Brown, T. Brunner, T. Dickel, J. Dilling, E. Dunling, J. Flowerdew, D. Fusco, et al., Exploring the nuclear chart via precision mass spectrometry with the TITAN MR-TOF MS, Atoms 13, 6 (2025).
  8. P. F. Giesel, M. Benhatchi, A. Arcones, D. Atanasov, K. Blaum, R. B. Cakirli, J. Karthein, D. Lange, Y. A. Litvinov, D. Lunney, V. Manea, M. Mougeot, S. Naimi, L. Nies, C. Schweiger, L. Schweikhard, and F. Wienholtz, Mass measurements of neutron-rich Ag and In isotopes for r-process nucleosynthesis studies, Technical Report No. CERN-INTC-2024-061, INTC-P-716 (CERN, Geneva, 2024).
  9. A. Boehnlein, M. Diefenthaler, N. Sato, M. Schram, V. Ziegler, C. Fanelli, M. Hjorth-Jensen, T. Horn, M. P. Kuchera, D. Lee, W. Nazarewicz, P. Ostroumov, K. Orginos, A. Poon, X.-N. Wang, A. Scheinker, M. S. Smith, and L.-G. Pang, Colloquium: Machine learning in nuclear physics, Rev. Mod. Phys. 94, 031003 (2022).
  10. W. J. Huang, M. Wang, F. G. Kondev, G. Audi, and S. Naimi, The AME 2020 atomic mass evaluation (I). Evaluation of input data, and adjustment procedures, Chin. Phys. C 45, 030002 (2021).
  11. G. Audi, The history of nuclidic masses and of their evaluation, Int. J. Mass Spectrom. 251, 85 (2006).
  12. A. H. Wapstra, G. Audi, and C. Thibault, The Ame2003 atomic mass evaluation, Nucl. Phys. A 729, 129 (2003).
  13. H. A. Bethe and R. F. Bacher, Nuclear Physics A. Stationary states of nuclei, Rev. Mod. Phys. 8, 82 (1936).
  14. A. Bhagwat, Simple nuclear mass formula, Phys. Rev. C 90, 064306 (2014).
  15. P. Möller, A. J. Sierk, T. Ichikawa, and H. Sagawa, Nuclear ground-state masses and deformations: FRDM(2012), At. Data Nucl. Data Tables 109–110, 1 (2016).
  16. J. Duflo and A. P. Zuker, Microscopic mass formulas, Phys. Rev. C 52, R23 (1995).
  17. N. Wang, M. Liu, X. Wu, and J. Meng, Surface diffuseness correction in global mass formula, Phys. Lett. B 734, 215 (2014).
  18. N. N. Ma, H. F. Zhang, X. J. Bao, and H. F. Zhang, Basic characteristics of nuclear landscape by improved Weizsäcker-Skyrme-type nuclear mass model, Chin. Phys. C 43, 044105 (2019).
  19. Y. Aboussir, J. M. Pearson, A. K. Dutta, and F. Tondeur, Nuclear mass formula via an approximation to the Hartree–Fock method, At. Data Nucl. Data Tables 61, 127 (1995).
  20. S. Goriely, N. Chamel, and J. M. Pearson, Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XIII. The 2012 atomic mass evaluation and the symmetry coefficient, Phys. Rev. C 88, 024308 (2013).
  21. D. Vretenar, A. V. Afanasjev, G. A. Lalazissis, and P. Ring, Relativistic Hartree–Bogoliubov theory: Static and dynamic aspects of exotic nuclear structure, Phys. Rep. 409, 101 (2005).
  22. S.-G. Zhou, Multidimensionally constrained covariant density functional theories—Nuclear shapes and potential energy surfaces, Phys. Scr. 91, 063008 (2016).
  23. P. Ring, Relativistic mean field theory in finite nuclei, Prog. Part. Nucl. Phys. 37, 193 (1996).
  24. J. S. Zheng, N. Y. Wang, Z. Y. Wang, Z. M. Niu, Y. F. Niu, and B. Sun, Mass predictions of the relativistic mean-field model with the radial basis function approach, Phys. Rev. C 90, 014303 (2014).
  25. R. Utama and J. Piekarewicz, Refining mass formulas for astrophysical applications: A Bayesian neural network approach, Phys. Rev. C 96, 044308 (2017).
  26. M. Mumpower, R. Surman, G. McLaughlin, and A. Aprahamian, The impact of individual nuclear properties on r-process nucleosynthesis, Prog. Part. Nucl. Phys. 86, 86 (2016).
  27. R. Utama, J. Piekarewicz, and H. Prosper, Nuclear mass predictions for the crustal composition of neutron stars: A Bayesian neural network approach, Phys. Rev. C 93, 014311 (2016).
  28. E. Yüksel, D. Soydaner, and H. Bahtiyar, Nuclear mass predictions using machine learning models, Phys. Rev. C 109, 064322 (2024).
  29. Z. Niu and H. Liang, Nuclear mass predictions with machine learning reaching the accuracy required by r-process studies, Phys. Rev. C 106, L021303 (2022).
  30. Y. Huang, J. Chen, J. Jia, L. M. Liu, Y. G. Ma, and C. Zhang, Validation and extrapolation of atomic masses with a physics-informed fully connected neural network, Phys. Rev. C 111, 034329 (2025).
  31. G. P. Liu, H. L. Wang, Z. Z. Zhang, and M. L. Liu, Model-repair capabilities of tree-based machine-learning algorithms applied to theoretical nuclear mass models, Phys. Rev. C 111, 024306 (2025).
  32. W. Ye and N. Wan, Understanding on prediction differences among theoretical mass models with machine learning techniques, Phys. Rev. C 111, 044317 (2025).
  33. Y. Saito, I. Dillmann, R. Kruecken, M. R. Mumpower, and R. Surman, Uncertainty quantification of mass models using ensemble Bayesian model averaging, Phys. Rev. C 109, 054301 (2024).
  34. V. Kejzlar, L. Neufcourt, and W. Nazarewicz, Local Bayesian Dirichlet mixing of imperfect models, Sci. Rep. 13, 19600 (2023).
  35. E. Alhassan, D. Rochman, G. Schnabel, and A. J. Koning, Bayesian model averaging (BMA) for nuclear data evaluation, Nucl. Sci. Tech. 35, 205 (2024).
  36. S. P. Adam, S.-A. N. Alexandropoulos, P. M. Pardalos, and M. N. Vrahatis, No free lunch theorem: A review, in Approximation and Optimization: Algorithms, Complexity and Applications, edited by I. C. Demetriou and P. M. Pardalos (Springer, Cham, 2019), pp. 57–82.
  37. L.-G. Pang, Studying high-energy nuclear physics with machine learning, Int. J. Mod. Phys. E 33, 2430009 (2024).
  38. I. Bentley, J. Tedder, M. Gebran, and A. Paul, High precision binding energies from physical-feature-instructed machine learning, Phys. Rev. C 111, 034305 (2025).
  39. J. H. Friedman, Greedy function approximation: A gradient boosting machine, Ann. Stat. 29, 1189 (2001).
  40. Z. P. Gao, Y. J. Wang, H. L. Lü, Q. F. Li, C. W. Shen, and L. Liu, Machine learning the nuclear mass, Nucl. Sci. Tech. 32, 109 (2021).
  41. L. W. Rizkallah, Enhancing the performance of gradient boosting trees on regression problems, J. Big Data 12, 35 (2025).
  42. J. H. Friedman, Stochastic gradient boosting, Comput. Stat. Data Anal. 38, 367 (2002).
  43. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, et al., Scikit-learn: Machine Learning in Python, J. Mach. Learn. Res. 12, 2825 (2011).
  44. M. Kortelainen, J. McDonnell, W. Nazarewicz, P.-G. Reinhard, J. Sarich, N. Schunck, M. Stoitsov, and S. Wild, Nuclear energy density optimization: Large deformations, Phys. Rev. C 85, 024304 (2012).
  45. L. S. Geng, H. Toki, S. Sugimoto, and J. Meng, Relativistic mean field theory for deformed nuclei with pairing correlations, Prog. Theor. Phys. 110, 921 (2003).
  46. L. S. Geng, Ground state properties of finite nuclei in the relativistic mean field model, Ph.D. thesis, Research Center for Nuclear Physics (RCNP), Osaka University, 2005.
  47. D. C. Montgomery, E. A. Peck, and G. G. Vining, Model adequacy checking, in Introduction to Linear Regression Analysis, 5th ed. (John Wiley & Sons, New Jersey, 2021), Chap. 4, pp. 134–169.
  48. See Supplemental Material at http://link.aps.org/supplemental/10.1103/8n1w-f3b7 for the complete ELMA nuclear mass table.
  49. https://ddnp.in.

Outline

Information

APS Open Sci. 1, 000085– Published 6 August, 2026
Vol. 1
  • Received 10 April 2026
  • Accepted 14 July 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation