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Interpretable neural network predictions of high-intensity femtosecond x-ray free-electron laser pulses using sulfur K-shell emission spectra

Harald Agelii1, Alfredo Bellisario1, Carl Caleman1,2, Nicusor Timneanu1,*, and Sebastian Cardoch1,†

  • *Contact author: nicusor.timneanu@physics.uu.se
  • †Contact author: sebastian.cardoch@physics.uu.se
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Phys. Rev. Research 7, 033066 – Published 17 July, 2025

DOI: https://doi.org/10.1103/dwc6-7hvn

Abstract

The emergence of high-intensity femtosecond duration x-rays from Free-Electron Lasers has enriched our understanding of the structure and dynamics of biological molecules at the atomic level. In serial femtosecond crystallography experiments, the magnitude of the interaction between photons and matter can vary significantly due to variations in the x-ray pulse's intensity, energy bandwidth and duration, as well as fluctuations in the synchronicity between the x-ray pulse and the sample. Accurate characterization of the conditions from each exposure is valuable for experiment and theory. In this theoretical work, we propose using x-ray emission spectra emanating from sulfur atoms, which are prevalent in biomolecules, to obtain individual hit information. We train a neural network based on synthetic K-shell emission spectra from a lysozyme crystal to predict x-ray fluence and pulse duration. The model achieves a training relative error of <12% when predicting both parameters concurrently. We use interpretation methods to identify the regions in the spectra that have the most predictive power. For fluence predictions, the model emphasizes K-L emission shifts to higher energies due to the presence of highly charged sulfur ions. For pulse duration predictions, the model places a greater focus on the emission signal from double core hole K-L emission. These results demonstrate that it is possible to predict x-ray exposure information on the sample based on physically interpretable features in sulfur's K-shell emission spectra.

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Phys. Rev. Research 7, 033066– Published 17 July, 2025
  • Received 8 March 2025
  • Accepted 23 June 2025
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