- Physical Review Journals
All JournalsPhysics Magazine

Physical Review C

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

Machine learning for correlations of electromagnetic properties in ab initio calculations

Marco Knöll1,*, Marc L. Agel1, Tobias Wolfgruber1, Pieter Maris2, and Robert Roth1,3,†

  • 1Institut für Kernphysik, Fachbereich Physik, Technische Universität Darmstadt, Schlossgartenstrasse 2, 64289 Darmstadt, Germany
  • 2Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
  • 3Helmholtz Forschungsakademie Hessen für FAIR, GSI Helmholtzzentrum, 64289 Darmstadt, Germany

  • *Contact author: marco.knoell@physik.tu-darmstadt.de
  • †Contact author: robert.roth@physik.tu-darmstadt.de
PDF

Phys. Rev. C 112, 034306 – Published 5 September, 2025

DOI: https://doi.org/10.1103/frfs-xz86

Abstract

In ab initio nuclear structure theory, accurately predicting electromagnetic observables, such as moments and transition rates, is essential for a comprehensive understanding of nuclear properties. However, computational limitations and conceptual difficulties often hinder the precise calculation of these observables. In this work, we extend machine learning methods for model-space extrapolations to electric quadrupole moments. We further present a new machine learning approach that leverages the correlations between energies, radii, and electromagnetic observables. By learning these correlations from no-core shell model calculations in accessible model spaces, this new model enables the prediction of electromagnetic observables in the full Hilbert space from predictions of full-space energies and radii, which can be obtained with established machine learning extrapolation tools. An essential property of our approach is the capability of uncertainty quantification, allowing for reliable predictions with combined statistical error estimates for many-body and interaction uncertainties. Being solely built upon the physical correlations of different observables, it can be generalized across different ab initio methods. We demonstrate the power of this new extrapolation scheme through a precision study of electric quadrupole moments across a wide range of p-shell nuclei.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (47)

  1. N. M. Parzuchowski, S. R. Stroberg, P. Navrátil, H. Hergert, and S. K. Bogner, Ab initio electromagnetic observables with the in-medium similarity renormalization group, Phys. Rev. C 96, 034324 (2017).
  2. K. Vobig, Electromagnetic observables and open-shell nuclei from the in-medium no-core shell model, Ph.D. thesis, Technische Universität Darmstadt, 2020.
  3. S. R. Stroberg, J. Henderson, G. Hackman, P. Ruotsalainen, G. Hagen, and J. D. Holt, Systematics of E2 strength in the sd shell with the valence-space in-medium similarity renormalization group, Phys. Rev. C 105, 034333 (2022).
  4. F. Bonaiti, S. Bacca, G. Hagen, and G. R. Jansen, Electromagnetic observables of open-shell nuclei from coupled-cluster theory, Phys. Rev. C 110, 044306 (2024).
  5. R. Roth and M. Petri, Electromagnetic properties of nuclei from first principles: A case for synergies between experiment and theory, Philos. Trans. A 382, 20230119 (2024).
  6. S. Baroni, P. Navrátil, and S. Quaglioni, Unified ab initio approach to bound and unbound states: No-core shell model with continuum and its application to 7He, Phys. Rev. C 87, 034326 (2013).
  7. P. Navrátil, S. Quaglioni, I. Stetcu, and B. Barrett, Recent developments in no-core shell-model calculations, J. Phys. G: Nucl. Part. Phys. 36, 083101 (2009).
  8. R. Roth, Importance truncation for large-scale configuration interaction approaches, Phys. Rev. C 79, 064324 (2009).
  9. D. C. Zheng, B. R. Barrett, L. Jaqua, J. P. Vary, and R. J. McCarthy, Microscopic calculations of the spectra of light nuclei, Phys. Rev. C 48, 1083 (1993).
  10. C Forssén, R. Roth, and P. Navrátil, Systematics of 2+ states in C isotopes from the no-core shell model, J. Phys. G: Nucl. Part. Phys. 40, 055105 (2013).
  11. P. Maris, J. P. Vary, and A. M. Shirokov, Ab initio no-core full configuration calculations of light nuclei, Phys. Rev. C 79, 014308 (2009).
  12. S. K. Bogner, R. J. Furnstahl, P. Maris, R. J. Perry, A. Schwenk, and J. P. Vary, Convergence in the no-core shell model with low-momentum two-nucleon interactions, Nucl. Phys. A 801, 21 (2008).
  13. R. J. Furnstahl, G. Hagen, and T. Papenbrock, Corrections to nuclear energies and radii in finite oscillator spaces, Phys. Rev. C 86, 031301(R) (2012).
  14. S. A. Coon, M. I. Avetian, M. K. G. Kruse, U. van Kolck, P. Maris, and J. P. Vary, Convergence properties of ab initio calculations of light nuclei in a harmonic oscillator basis, Phys. Rev. C 86, 054002 (2012).
  15. S. N. More, A. Ekström, R. J. Furnstahl, G. Hagen, and T. Papenbrock, Universal properties of infrared oscillator basis extrapolations, Phys. Rev. C 87, 044326 (2013).
  16. R. J. Furnstahl, S. N. More, and T. Papenbrock, Systematic expansion for infrared oscillator basis extrapolations, Phys. Rev. C 89, 044301 (2014).
  17. K. A. Wendt, C. Forssén, T. Papenbrock, and D. Sääf, Infrared length scale and extrapolations for the no-core shell model, Phys. Rev. C 91, 061301(R) (2015).
  18. G. A. Negoita, J. P. Vary, G. R. Luecke, P. Maris, A. M. Shirokov, I. J. Shin, Y. Kim, E. G. Ng, C. Yang, M. Lockner, and G. M. Prabhu, Deep learning: Extrapolation tool for ab initio nuclear theory, Phys. Rev. C 99, 054308 (2019).
  19. W. G. Jiang, G. Hagen, and T. Papenbrock, Extrapolation of nuclear structure observables with artificial neural networks, Phys. Rev. C 100, 054326 (2019).
  20. M. Knöll, T. Wolfgruber, M. L. Agel, C. Wenz, and R. Roth, Machine learning for the prediction of converged energies from ab initio nuclear structure calculations, Phys. Lett. B 839, 137781 (2023).
  21. T. Wolfgruber, M. Knöll, and R. Roth, Precise neural network predictions of energies and radii from the no-core shell model, Phys. Rev. C 110, 014327 (2024).
  22. M. A. Caprio, P. J. Fasano, and P. Maris, Robust ab initio prediction of nuclear electric quadrupole observables by scaling to the charge radius, Phys. Rev. C 105, L061302 (2022).
  23. M. A. Caprio and P. Maris, Robust ab initio predictions for dimensionless ratios of E2 and radius observables. I. Electric quadrupole moments and deformation, arXiv:2409.03926.
  24. J. A. Melendez, R. J. Furnstahl, D. R. Phillips, M. T. Pratola, and S. Wesolowski, Quantifying correlated truncation errors in effective field theory, Phys. Rev. C 100, 044001 (2019).
  25. R. Machleidt and D. R. Entem, Chiral effective field theory and nuclear forces, Phys. Rep. 503, 1 (2011).
  26. E. Epelbaum, H.-W. Hammer, and Ulf-G. Meißner, Modern theory of nuclear forces, Rev. Mod. Phys. 81, 1773 (2009).
  27. T. Hüther, K. Vobig, K. Hebeler, R. Machleidt, and R. Roth, Family of chiral two-plus three-nucleon interactions for accurate nuclear structure studies, Phys. Lett. B 808, 135651 (2020).
  28. P. Maris, E. Epelbaum, R. J. Furnstahl, J. Golak, K. Hebeler, T. Hüther, H. Kamada, H. Krebs, Ulf-G. Meißner, J. Melendez et al., Light nuclei with semilocal momentum-space regularized chiral interactions up to third order, Phys. Rev. C 103, 054001 (2021).
  29. H. Hergert, S. K. Bogner, S. Binder, A. Calci, J. Langhammer, R. Roth, and A. Schwenk, In-medium similarity renormalization group with chiral two- plus three-nucleon interactions, Phys. Rev. C 87, 034307 (2013).
  30. S. K. Bogner, R. J. Furnstahl, and R. J. Perry, Similarity renormalization group for nucleon-nucleon interactions, Phys. Rev. C 75, 061001(R) (2007).
  31. S. K. Bogner, R. J. Furnstahl, and A. Schwenk, From low-momentum interactions to nuclear structure, Prog. Part. Nucl. Phys. 65, 94 (2010).
  32. R. Roth, T. Neff, and H. Feldmeier, Nuclear structure in the framework of the unitary correlation operator method, Prog. Part. Nucl. Phys. 65, 50 (2010).
  33. R. J. Furnstahl and K. Hebeler, New applications of renormalization group methods in nuclear physics, Rep. Prog. Phys. 76, 126301 (2013).
  34. R. Roth, A. Calci, J. Langhammer, and S. Binder, Evolved chiral NN+3N Hamiltonians for ab initio nuclear structure calculations, Phys. Rev. C 90, 024325 (2014).
  35. I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (MIT Press, Cambridge, 2016).
  36. R. Rojas, The backpropagation algorithm, Neural Networks (Springer, Berlin, 1996), pp. 149–182.
  37. D. R. Entem, R. Machleidt, and Y. Nosyk, High-quality two-nucleon potentials up to fifth order of the chiral expansion, Phys. Rev. C 96, 024004 (2017).
  38. I. Loshchilov and F. Hutter, Decoupled weight decay regularization, arXiv:1711.05101.
  39. V. Nair and G. E. Hinton, Rectified linear units improve restricted boltzmann machines, in ICML'10: Proceedings of the 27th International Conference on International Conference on Machine Learning (ACM, New York, 2010).
  40. D. Freedman and P. Diaconis, On the histogram as a density estimator: L2 theory, Probab. Theory Relat. Fields 57, 453 (1981).
  41. M. Knöll, M. Lockner, P. Maris, R. J. McCarty, R. Roth, J. P. Vary, and T. Wolfgruber, Benchmarking artificial neural network extrapolations of the ground-state energies and radii of Li isotopes, Phys. Rev. C 111, 064304 (2025).
  42. N. J. Stone, Table of nuclear electric quadrupole moments, At. Data Nucl. Data Tables 111–112, 1 (2016).
  43. T. Wolfgruber, T. Gesser, M. Knöll, P. Maris, and R. Roth, High-precision ab initio radius calculations of boron isotopes, Phys. Rev. C 112, 014306 (2025).
  44. P. Reinert, H. Krebs, and E. Epelbaum, Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order, Eur. Phys. J. A 54, 86 (2018).
  45. P. Maris, R. Roth, E. Epelbaum, R. Furnstahl, J. Golak, K. Hebeler, T. Hüther, H. Kamada, H. Krebs, H. Le, U.-G. Meißner, J. Melendez, A. Nogga, P. Reinert, R. Skibiński, J. Vary, H. Witała, and T. Wolfgruber (LENPIC Collaboration), Nuclear properties with semilocal momentum-space regularized chiral interactions beyond N2LO, Phys. Rev. C 106, 064002 (2022).
  46. H. M. Aktulga, C. Yang, E. G. Ng, P. Maris, and J. P. Vary, Improving the scalability of a symmetric iterative eigensolver for multi-core platforms, Concurr. Comput. Pract. Exp. 26, 2631 (2014).
  47. M. Shao, H. M. Aktulga, C. Yang, E. G. Ng, P. Maris, and J. P. Vary, Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver, Comput. Phys. Commun. 222, 1 (2018).

Outline

Information

Phys. Rev. C 112, 034306– Published 5 September, 2025
  • Received 16 January 2025
  • Accepted 8 August 2025
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