Abstract
Atomic data determined by analysis of observed atomic spectra are essential for plasma diagnostics. For each low-ionisation open d- and f-subshell atomic species, around 103 fine structure energy levels can be determined through years of analysis of 104 observable spectral lines. We propose a partial automation of this task by casting the analysis procedure as a Markov decision process and solving it by graph reinforcement learning using reward functions partly learned on historical human decisions. In our evaluations on existing spectral line lists and theoretical calculations for Co II, Nd II and Nd III, hundreds of energy levels were identified and determined in hours, agreeing with published values in 95% of cases for Co II and 54–87% for Nd II and Nd III. As the current efficiency in atomic fine structure determination struggles to meet growing atomic data demands, our artificial intelligence approach sets the stage for closing this gap.
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All data used to generate results in this paper are made available on Zenodo (https://doi.org/10.5281/zenodo.18452552) and at the GitHub repository.
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All code used to generate results in this paper is made available on Zenodo (https://doi.org/10.5281/zenodo.18452552) and at the GitHub repository.
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Acknowledgements
M.D. and J.C.P. acknowledge support from the Science and Technology Facilities Council (STFC) of the UK under grant numbers ST/N000939/1, ST/S000372/1, ST/W000989/1, and UKRI1188, and The Bequest of Prof. Edward Steers. V.-A.D. and N.H. acknowledge support from the Natural Environment Research Council (NERC) Twinning Capability for the Natural Environment (TWINE) Programme NE/Z503381/1, the Engineering and Physical Sciences Research Council (EPSRC) From Sensing to Collaboration Programme Grant EP/V000748/1, and the Innovate UK AutoInspect Grant 1004416. A.N.R is grateful to the late Dr J.-F. Wyart for help in Nd II calculations and to the support from research project FFUU-2025-0005 of the Institute of Spectroscopy of the Russian Academy of Sciences.
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M.D. – planning, method design, execution, Co II calculations, manuscript preparation. V.-A.D. – planning, method design, manuscript preparation. A.N.R. – Nd II-III calculations, and manuscript review. N.H. – resource management, manuscript review. J.C.P. – resource management, progress and manuscript review.
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Communications Physics thanks Andreas Flörs, Ricardo Ferreira da Silva, Alexander Kramida and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Ding, M., Darvariu, VA., Ryabtsev, A.N. et al. Accelerating atomic fine structure determination with graph reinforcement learning. Commun Phys (2026). https://doi.org/10.1038/s42005-026-02582-y
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DOI: https://doi.org/10.1038/s42005-026-02582-y
