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Learning nuclear cross sections across the chart of nuclides with graph neural networks

Hongjun Choi1,*, Sinjini Mitra2, Jason Brodksy1, Ruben Glatt1, Erika Holmbeck1, Shusen Liu1, Nicolas Schunck1, Andre Sieverding1, and Kyle Wendt1

  • *Contact author: choi22@llnl.gov
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Phys. Rev. C 112, 044601 – Published 1 October, 2025

DOI: https://doi.org/10.1103/4jd4-bnyh

Abstract

We explore the use of deep learning techniques to learn how nuclear cross sections change as we add or remove protons and neutrons. As a proof of principle, we focus on the neutron-induced reactions in the fast energy regime. Our approach follows a two-stage learning framework. First, we apply representation learning to encode cross section data into a latent space using either variational autoencoders (VAEs) or implicit neural representations (INRs). Then, we train graph neural networks (GNNs) on the resulting embeddings to predict missing values across the nuclear chart by leveraging the topological structure of neighboring isotopes. We demonstrate accurate cross section predictions within a 9×9 block of missing nuclei. We also find that the optimal GNN training strategy depends on the type of latent representation used, with VAE embeddings performing best under end-to-end optimization in the original space, while INR embeddings achieve better results when the GNN is trained only in the latent space. Furthermore, using clustering algorithms, we map groups of latent vectors into regions of the nuclear chart and show that VAEs and INRs can discover some of the neutron magic numbers. These findings suggest that deep-learning models based on the representation encoding of cross sections combined with graph neural networks hold significant potential in augmenting nuclear theory models, e.g., by providing reliable estimates of covariances of cross sections, including cross-material covariances.

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References (44)

  1. J. Blatt and V. Weisskopf, Theoretical Nuclear Physics (Springer-Verlag, New York, 1979).
  2. O. Iwamoto, N. Iwamoto, S. Kunieda, F. Minato, S. Nakayama, Y. Abe, K. Tsubakihara, S. Okumura, C. Ishizuka, T. Yoshida, S. Chiba, N. Otuka, J.-C. Sublet, H. Iwamoto, K. Yamamoto, Y. Nagaya, K. Tada, C. Konno, N. Matsuda, K. Yokoyama et al., Japanese evaluated nuclear data library version 5: JENDL-5, J. Nucl. Sci. Technol. 60, 1 (2023).
  3. A. J. M. Plompen, O. Cabellos, C. De Saint Jean, M. Fleming, A. Algora, M. Angelone, P. Archier, E. Bauge, O. Bersillon, A. Blokhin, F. Cantargi, A. Chebboubi, C. Diez, H. Duarte, E. Dupont, J. Dyrda, B. Erasmus, L. Fiorito, U. Fischer et al., The joint evaluated fission and fusion nuclear data library, JEFF-3.3, Eur. Phys. J. A 56, 181 (2020).
  4. D. A. Brown, M. B. Chadwick, R. Capote, A. C. Kahler, A. Trkov, M. W. Herman, A. A. Sonzogni, Y. Danon, A. D. Carlson, M. Dunn, D. L. Smith, G. M. Hale, G. Arbanas, R. Arcilla, C. R. Bates, B. Beck, B. Becker, F. Brown, R. J. Casperson, J. Conlin et al., ENDF/B-VIII.0: The 8th major release of the nuclear reaction data library with CIELO-project cross sections, new standards and thermal scattering data, Nucl. Data Sheets 148, 1 (2018).
  5. L. Bernstein, F. Bostelmann, M. Carpenter, M. Chadwick, M. Fratoni, A. Hawari, L. Heilbronn, C. Howell, J. Ressler, C. Keppel, A. Koning, K. LaBel, T. Turflinger, C. Nesaraja, S. Qaim, C. Romano, A. Spyrou, S. Siem, C. Vermeulen, and R. Vogt, First Report of the Nuclear Data Subcommittee of the Nuclear Science Advisory Committee, Technical Report No. LLNL-TR-840465, 1890079, 1061532 (Lawrence Livermore National Laboratory, Livermore, CA, 2022).
  6. F. Bolstelmann, G. Ilas, C. Celik, A. Holcomb, and W. Wiesequist, Nuclear Data Assessment for Advanced Reactors, Technical Report No. UREG/CR-7289, ORNL/TM-2021/2002 (United States Nuclear Regulatory Commission, Washington, DC, 2022).
  7. M. U. Khandaker, D. A. Bradley, H. Osman, M. I. Sayyed, A. Sulieman, M. R. I. Faruque, K. A. Naseer, and A. M. Idris, The significance of nuclear data in the production of radionuclides for theranostic/therapeutic applications, Radiat. Phys. Chem. 200, 110342 (2022), special issue, The 15th International Symposium on Radiation Physics (ISRP15), 6–10 December 2021, Sunway University, Malaysia.
  8. A. C. Hayes, Applications of nuclear physics, Rep. Prog. Phys. 80, 026301 (2017).
  9. I. U. Roederer, N. Vassh, E. M. Holmbeck, M. R. Mumpower, R. Surman, J. J. Cowan, T. C. Beers, R. Ezzeddine, A. Frebel, T. T. Hansen, V. M. Placco, and C. M. Sakari, Element abundance patterns in stars indicate fission of nuclei heavier than uranium, Science 382, 1177 (2023).
  10. M. R. Mumpower, R. Surman, G. C. McLaughlin, and A. Aprahamian, The impact of individual nuclear properties on r-process nucleosynthesis, Prog. Part. Nucl. Phys. 86, 86 (2016).
  11. G. Dodge, A New Era of Discovery: The 2023 Long-Range Plan for Nuclear Science, Technical Report (U.S. Department of Energy and National Science Foundation, Washington, DC, 2023).
  12. I. J. Thompson and F. M. Nunes, Nuclear Reactions for Astrophysics: Principles, Calculation and Applications of Low-Energy Reactions (Cambridge University Press, Cambridge, 2009).
  13. P. Navrátil and S. Quaglioni, Ab initio nuclear reaction theory with applications to astrophysics, in Handbook of Nuclear Physics, edited by I. Tanihata, H. Toki, and T. Kajino (Springer Nature, Singapore, 2020), p. 1.
  14. P. E. Hodgson, Compound nucleus reactions, Rep. Prog. Phys. 50, 1171 (1987).
  15. B. V. Carlson, J. E. Escher, and M. S. Hussein, Theoretical descriptions of compound-nuclear reactions: Open problems and challenges, J. Phys. G: Nucl. Part. Phys. 41, 094003 (2014).
  16. R. Capote, M. Herman, P. Obložinský, P. G. Young, S. Goriely, T. Belgya, A. V. Ignatyuk, A. J. Koning, S. Hilaire, V. A. Plujko, M. Avrigeanu, O. Bersillon, M. B. Chadwick, T. Fukahori, Z. Ge, Y. Han, S. Kailas, J. Kopecky, V. M. Maslov, G. Reffo, M. Sin, E.Sh. Soukhovitskii, and P. Talou, RIPL–reference input parameter library for calculation of nuclear reactions and nuclear data evaluations, Nucl. Data Sheets 110, 3107 (2009).
  17. S. Goriely, P. Dimitriou, M. Wiedeking, T. Belgya, R. Firestone, J. Kopecky, M. Krtička, V. Plujko, R. Schwengner, S. Siem, H. Utsunomiya, S. Hilaire, S. Péru, Y. S. Cho, D. M. Filipescu, N. Iwamoto, T. Kawano, V. Varlamov, and R. Xu, Reference database for photon strength functions, Eur. Phys. J. A 55, 172 (2019).
  18. K. Kolos, V. Sobes, R. Vogt, C. E. Romano, M. S. Smith, L. A. Bernstein, D. A. Brown, M. T. Burkey, Y. Danon, M. A. Elsawi, B. L. Goldblum, L. H. Heilbronn, S. L. Hogle, J. Hutchinson, B. Loer, E. A. McCutchan, M. R. Mumpower, E. M. O'Brien, C. Percher, P. N. Peplowski et al., Current nuclear data needs for applications, Phys. Rev. Res. 4, 021001 (2022).
  19. M. D. Schwartz, Modern machine learning and particle physics, Harvard Data Sci. Rev. 3, 13 (2021).
  20. M. Feickert and B. Nachman, A living review of machine learning for particle physics, arXiv:2102.02770.
  21. J. M. R. Fox and K. A. Wendt, Illuminating systematic trends in nuclear data with generative machine learning models, arXiv:2403.16389.
  22. M. M. Bronstein, J. Bruna, Y. LeCun, A. Szlam, and P. Vandergheynst, Geometric deep learning: going beyond Euclidean data, IEEE Signal Process. Mag. 34, 18 (2017).
  23. F. Scarselli, M. Gori, A. C. Tsoi, M. Hagenbuchner, and G. Monfardini, The graph neural network model, IEEE Trans. Neural Netw. 20, 61 (2008).
  24. X. Ju, S. Farrell, P. Calafiura, D. Murnane, L. Gray, T. Klijnsma, K. Pedro, G. Cerati, J. Kowalkowski, G. Perdue et al., Graph neural networks for particle reconstruction in high energy physics detectors, arXiv:2003.11603.
  25. C. Doersch, Tutorial on variational autoencoders, arXiv:1606.05908.
  26. A. Koning, S. Hilaire, and S. Goriely, Talys: modeling of nuclear reactions, Eur. Phys. J. A 59, 131 (2023).
  27. M. Herman, R. Capote, B. V. Carlson, P. Obložinský, M. Sin, A. Trkov, H. Wienke, and V. Zerkin, EMPIRE: Nuclear reaction model code system for data evaluation, Nucl. Data Sheets 108, 2655 (2007), Special Issue on Evaluations of Neutron Cross Sections.
  28. M. Bender, P.-H. Heenen, and P.-G. Reinhard, Self-consistent mean-field models for nuclear structure, Rev. Mod. Phys. 75, 121 (2003).
  29. A. J. Koning, D. Rochman, J. C. Sublet, N. Dzysiuk, M. Fleming, and S. van der Marck, TENDL: Complete nuclear data library for innovative nuclear science and technology, Nucl. Data Sheets 155, 1 (2019), Special Issue on Nuclear Reaction Data.
  30. D. P. Kingma and M. Welling, Auto-encoding variational bayes, in Proceeding of the 2nd International Conference on Learning Representations (ICLR, 2014).
  31. D. Ha, A. M. Dai, and Q. V. Le, Hypernetworks, arXiv:1609.09106.
  32. V. Sitzmann, J. Martel, A. Bergman, D. Lindell, and G. Wetzstein, Implicit neural representations with periodic activation functions, in Advances in Neural Information Processing Systems, edited by H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin (Curran Associates, Inc., 2020), Vol. 33, pp. 7462–7473.
  33. M. I. Jordan, Z. Ghahramani, T. S. Jaakkola, and L. K. Saul, An introduction to variational methods for graphical models, Mach. Learn. 37, 183 (1999).
  34. A. F. Agarap, Deep learning using rectified linear units (ReLU), arXiv:1803.08375.
  35. B. Mildenhall, P. P. Srinivasan, M. Tancik, J. T. Barron, R. Ramamoorthi, and R. Ng, NeRF: Representing scenes as neural radiance fields for view synthesis, Commun. ACM 65, 99 (2022).
  36. L. Mescheder, M. Oechsle, M. Niemeyer, S. Nowozin, and A. Geiger, Occupancy networks: Learning 3D reconstruction in function space, in Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (IEEE, Piscataway, NJ, 2019), pp. 4460–4470.
  37. F. Szatkowski, K. J. Piczak, P. Spurek, J. Tabor, and T. Trzciński, Hypernetworks build implicit neural representations of sounds, in Joint European Conference on Machine Learning and Knowledge Discovery in Databases (Springer, Berlin, 2023), pp. 661–676.
  38. J. Gilmer, S. S. Schoenholz, P. F. Riley, O. Vinyals, and G. E. Dahl, Neural message passing for quantum chemistry, in International Conference on Machine Learning (PMLR, 2017), Vol. 70, pp. 1263–1272.
  39. F. M. Bianchi, D. Grattarola, L. Livi, and C. Alippi, Graph neural networks with convolutional ARMA filters, IEEE Trans. Pattern Anal. Mach. Intell. 44, 3496 (2022).
  40. Y. Li, D. Tarlow, M. Brockschmidt, and R. Zemel, Gated graph sequence neural networks, arXiv:1511.05493.
  41. W. Hamilton, Z. Ying, and J. Leskovec, Inductive representation learning on large graphs, in NIPS'17: Proceedings of the 31st International Conference on Neural Information Processing Systems (Curran Associates, Reed Hook, NY, 2017).
  42. I. Loshchilov and F. Hutter, Decoupled weight decay regularization, in Proceedings of the 7th International Conference on Learning Representations (ICLR, 2019).
  43. L. N. Smith, A disciplined approach to neural network hyper-parameters: Part 1–learning rate, batch size, momentum, and weight decay, arXiv:1803.09820.
  44. L. van der Maaten and G. Hinton, Visualizing data using t-SNE, J. Mach. Learn. Res. 9, 2579 (2008).

Outline

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Phys. Rev. C 112, 044601– Published 1 October, 2025
  • Received 2 April 2024
  • Revised 28 April 2025
  • Accepted 22 August 2025
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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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