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 neutrino-nucleus cross sections

Daniel C. Hackett1,*, Joshua Isaacson1,2,†, Shirley Weishi Li3,‡, Karla Tame-Narvaez1,§, and Michael L. Wagman1,∥

  • *Contact author: dhackett@fnal.gov
  • †Contact author: isaacs21@msu.edu
  • ‡Contact author: shirley.li@uci.edu
  • §Contact author: karla@fnal.gov
  • ∥Contact author: mwagman@fnal.gov

Phys. Rev. D 112, 113005 – Published 24 December, 2025

DOI: https://doi.org/10.1103/bslk-gxr7

Abstract

Neutrino-nucleus scattering cross sections are critical theoretical inputs for long-baseline neutrino oscillation experiments. However, robust modeling of these cross sections remains challenging. For a simple but physically motivated toy model of the DUNE experiment, we demonstrate that an accurate neural-network model of the cross section—leveraging only Standard-Model symmetries—can be learned from near-detector data. We perform a neutrino oscillation analysis with simulated far-detector events, finding that oscillation analysis results enabled by our data-driven cross-section model approach the theoretical limit achievable with perfect prior knowledge of the cross section. We further quantify the effects of flux shape and detector resolution uncertainties as well as systematics from cross-section mismodeling. This proof-of-principle study highlights the potential of future neutrino near-detector datasets and data-driven cross-section models.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (89)

  1. F. An et al. (JUNO Collaboration), J. Phys. G 43, 030401 (2016).
  2. K. Abe et al. (Hyper-Kamiokande Collaboration), arXiv:1805.04163.
  3. B. Abi et al. (DUNE Collaboration), arXiv:2002.03005.
  4. L. Alvarez-Ruso et al. (NuSTEC Collaboration), Prog. Part. Nucl. Phys. 100, 1 (2018).
  5. L. A. Ruso et al., J. Phys. G 52, 043001 (2025).
  6. A. de Gouvêa et al., arXiv:2209.07983.
  7. A. M. Ankowski, O. Benhar, P. Coloma, P. Huber, C.-M. Jen, C. Mariani, D. Meloni, and E. Vagnoni, Phys. Rev. D 92, 073014 (2015).
  8. M. Khachatryan et al. (CLAS and e4v Collaborations), Nature (London) 599, 565 (2021).
  9. M. A. Acero et al. (NOvA Collaboration), Phys. Rev. D 106, 032004 (2022).
  10. K. Abe et al. (T2K Collaboration), Phys. Rev. D 103, 112008 (2021).
  11. K. Abe et al. (T2K Collaboration), Eur. Phys. J. C 83, 782 (2023).
  12. A. M. Ankowski, P. Coloma, P. Huber, C. Mariani, and E. Vagnoni, Phys. Rev. D 92, 091301 (2015).
  13. A. Friedland and S. W. Li, Phys. Rev. D 99, 036009 (2019).
  14. A. Friedland and S. W. Li, Phys. Rev. D 102, 096005 (2020).
  15. P. Abratenko et al. (MicroBooNE Collaboration), Phys. Rev. Lett. 128, 241801 (2022).
  16. P. Abratenko et al. (MicroBooNE Collaboration), Eur. Phys. J. C 84, 1052 (2024).
  17. C. Andreopoulos et al., Nucl. Instrum. Methods Phys. Res., Sect. A 614, 87 (2010).
  18. O. Buss, T. Gaitanos, K. Gallmeister, H. van Hees, M. Kaskulov, O. Lalakulich, A. B. Larionov, T. Leitner, J. Weil, and U. Mosel, Phys. Rep. 512, 1 (2012).
  19. T. Golan, J. T. Sobczyk, and J. Zmuda, Nucl. Phys. B, Proc. Suppl. 229–232, 499 (2012).
  20. L. Aliaga et al. (MINERvA Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 743, 130 (2014).
  21. Y. Hayato and L. Pickering, Eur. Phys. J. Spec. Top. 230, 4469 (2021).
  22. J. Isaacson, W. I. Jay, A. Lovato, P. A. N. Machado, and N. Rocco, Phys. Rev. D 107, 033007 (2023).
  23. P. Abratenko et al. (MicroBooNE Collaboration), Phys. Rev. Lett. 133, 041801 (2024).
  24. S. R. Beane, P. F. Bedaque, W. C. Haxton, D. R. Phillips, and M. J. Savage, 10.1142/9789812810458_0011 (2000).
  25. E. Epelbaum, H.-W. Hammer, and U.-G. Meissner, Rev. Mod. Phys. 81, 1773 (2009).
  26. D. B. Kaplan, Phys. Rev. C 102, 034004 (2020).
  27. H. W. Hammer, S. König, and U. van Kolck, Rev. Mod. Phys. 92, 025004 (2020).
  28. U. van Kolck, Front. Phys. 8, 79 (2020).
  29. E. Epelbaum, H. Krebs, and P. Reinert, Semi-local Nuclear Forces From Chiral EFT: State-of-the-Art and Challenges, in Handbook of Nuclear Physics, edited by I. Tanihata, H. Toki, and T. Kajino (Springer Nature, 2022), pp. 1–25.
  30. M. A. Acero et al. (NOvA Collaboration), Eur. Phys. J. C 80, 1119 (2020).
  31. P. Stowell et al. (MINERvA Collaboration), Phys. Rev. D 100, 072005 (2019).
  32. N. M. Coyle, S. W. Li, and P. A. N. Machado, J. High Energy Phys. 12 (2022) 166.
  33. R. D. Ball, V. Bertone, F. Cerutti, L. Del Debbio, S. Forte, A. Guffanti, J. I. Latorre, J. Rojo, and M. Ubiali (NNPDF Collaboration), Nucl. Phys. B855, 153 (2012).
  34. R. Abdul Khalek, J. J. Ethier, and J. Rojo (NNPDF Collaboration), Eur. Phys. J. C 79, 471 (2019).
  35. S. Forte, L. Garrido, J. I. Latorre, and A. Piccione, J. High Energy Phys. 05 (2002) 062.
  36. A. Candido, A. Garcia, G. Magni, T. Rabemananjara, J. Rojo, and R. Stegeman, J. High Energy Phys. 05 (2023) 149.
  37. J. E. Sobczyk, N. Rocco, and A. Lovato, Phys. Lett. B 859, 139142 (2024).
  38. C. M. Marshall, K. S. McFarland, and C. Wilkinson, Phys. Rev. D 101, 032002 (2020).
  39. K. Abe et al. (T2K Collaboration), Phys. Rev. D 95, 111101 (2017).
  40. P. A. Machado, O. Palamara, and D. W. Schmitz, Annu. Rev. Nucl. Part. Sci. 69, 363 (2019).
  41. W. Altmannshofer, S. Gori, J. Martín-Albo, A. Sousa, and M. Wallbank, Phys. Rev. D 100, 115029 (2019).
  42. A. de Gouvea, P. A. N. Machado, Y. F. Perez-Gonzalez, and Z. Tabrizi, Phys. Rev. Lett. 125, 051803 (2020).
  43. J. M. Berryman, A. de Gouvea, P. J. Fox, B. J. Kayser, K. J. Kelly, and J. L. Raaf, J. High Energy Phys. 02 (2020) 174.
  44. S. A. R. Ellis, K. J. Kelly, and S. W. Li, Phys. Rev. D 102, 115027 (2020).
  45. S. A. R. Ellis, K. J. Kelly, and S. W. Li, J. High Energy Phys. 12 (2020) 068.
  46. M. A. Acero et al. (NOvA Collaboration), Phys. Rev. Lett. 127, 201801 (2021).
  47. R. Acciarri et al. (ArgoNeuT Collaboration), Phys. Rev. Lett. 130, 221802 (2023).
  48. P. Abratenko et al. (MicroBooNE Collaboration), Phys. Rev. Lett. 132, 041801 (2024).
  49. P. Abratenko et al. (MicroBooNE Collaboration), Phys. Rev. Lett. 132, 241801 (2024).
  50. P. Coloma, J. Martín-Albo, and S. Urrea, Phys. Rev. D 109, 035013 (2024).
  51. C. H. Albright and C. Jarlskog, Nucl. Phys. B84, 467 (1975).
  52. E. A. Paschos and J. Y. Yu, Phys. Rev. D 65, 033002 (2002).
  53. S. Kretzer and M. H. Reno, Phys. Rev. D 66, 113007 (2002).
  54. O. Tomalak, Q. Chen, R. J. Hill, and K. S. McFarland, Nat. Commun. 13, 5286 (2022).
  55. O. Tomalak, Q. Chen, R. J. Hill, K. S. McFarland, and C. Wret, Phys. Rev. D 106, 093006 (2022).
  56. A. Afanasev et al., Eur. Phys. J. A 60, 91 (2024).
  57. J. D. Bjorken and E. A. Paschos, Phys. Rev. 185, 1975 (1969).
  58. C. G. Callan, Jr. and D. J. Gross, Phys. Rev. Lett. 22, 156 (1969).
  59. T.-J. Hou et al., Phys. Rev. D 103, 014013 (2021).
  60. A. Buckley, J. Ferrando, S. Lloyd, K. Nordström, B. Page, M. Rüfenacht, M. Schönherr, and G. Watt, Eur. Phys. J. C 75, 132 (2015).
  61. A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt, Eur. Phys. J. C 63, 189 (2009).
  62. R. Ruiz et al., Prog. Part. Nucl. Phys. 136, 104096 (2024).
  63. L. Fields,DUNE Fluxes, https://glaucus.crc.nd.edu/DUNEFluxes/.
  64. I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, J. P. Pinheiro, and T. Schwetz, J. High Energy Phys. 12 (2024) 216.
  65. P. B. Denton and S. J. Parke, Phys. Rev. D 110, 073005 (2024).
  66. S. Kullback and R. A. Leibler, Ann. Math. Stat. 22, 79 (1951).
  67. D. P. Kingma and J. Ba, arXiv:1412.6980.
  68. B. Efron, The Jackknife, the Bootstrap and Other Resampling Plans, Regional Conference Series in Applied Mathematics No. 38 (Society for Industrial and Applied Mathematics, Philadelphia, 1982).
  69. T. J. DiCiccio and B. Efron, Stat. Sci. 11, 189 (1996).
  70. A. C. Davison and D. V. Hinkley, The basic bootstraps, in Bootstrap Methods and their Application, Cambridge Series in Statistical and Probabilistic Mathematics (Cambridge University Press, Cambridge, England, 1997), pp. 11–69.
  71. V. Hewes et al. (DUNE Collaboration), Instruments 5, 31 (2021).
  72. N. Grant, Neutrino energy reconstruction in the DUNE far detector (2017), talk at the DPF meeting.
  73. C. Marshall, Physics performance of the DUNE “Day 1” Near Detector (2020), talk at TMS meeting.
  74. B. Abi et al. (DUNE Collaboration), Eur. Phys. J. C 80, 978 (2020).
  75. J. Arbel, K. Pitas, M. Vladimirova, and V. Fortuin, arXiv:2309.16314.
  76. G. J. Feldman and R. D. Cousins, Phys. Rev. D 57, 3873 (1998).
  77. N. M. Coyle, S. W. Li, and P. A. N. Machado, Phys. Rev. D 111, 093010 (2025).
  78. W. He, Z. Jiang, T. Xiao, Z. Xu, and Y. Li, arXiv:2302.13425.
  79. A. Accardi et al., Eur. Phys. J. A 52, 268 (2016).
  80. R. Abdul Khalek et al., Nucl. Phys. A1026, 122447 (2022).
  81. R. Abdul Khalek et al., arXiv:2203.13199.
  82. A. Paszke et al., in Advances in Neural Information Processing Systems 32, edited by H. Wallach, H. Larochelle, A. Beygelzimer, F. d’Alché-Buc, E. Fox, and R. Garnett (Curran Associates, Inc., Red Hook, NY, USA, 2019), pp. 8024–8035.
  83. C. R. Harris et al., Nature (London) 585, 357 (2020).
  84. P. Virtanen et al. (SciPy 1.0 Contributors), Nat. Methods 17, 261 (2020).
  85. J. Reback et al., pandas-dev/pandas: Pandas 1.0.3 (2020).
  86. Wes McKinney, in Proceedings of the 9th Python in Science Conference, edited by Stéfan van der Walt and Jarrod Millman (2010), pp. 56–61.
  87. G. P. Lepage, 10.5281/zenodo.4290884 (2020).
  88. Wolfram Research Inc., Mathematica, Version 14.0, https://www.wolfram.com/mathematica.
  89. J. D. Hunter, Comput. Sci. Eng. 9, 90 (2007).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation