Femtosecond pulse parameter estimation from photoelectron momenta using machine learning

Tomasz Szołdra, Marcelo F. Ciappina, Nicholas Werby, Philip H. Bucksbaum, Maciej Lewenstein, Jakub Zakrzewski, Andrew S. Maxwell*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Deep learning models have provided huge interpretation power for image-like data. Specifically, convolutional neural networks (CNNs) have demonstrated incredible acuity for tasks such as feature extraction or parameter estimation. Here we test CNNs on strong-field ionization photoelectron spectra, training on theoretical data sets to 'invert' experimental data. Pulse characterization is used as a 'testing ground', specifically we retrieve the laser intensity, where 'traditional' measurements typically lead to 20% uncertainty. We report on crucial data augmentation techniques required to successfully train on theoretical data and return consistent results from experiments, including accounting for detector saturation. The same procedure can be repeated to apply CNNs in a range of scenarios for strong-field ionization. Using a predictive uncertainty estimation, reliable laser intensity uncertainties of a few percent can be extracted, which are consistently lower than those given by traditional techniques. Using interpretability methods can reveal parts of the distribution that are most sensitive to laser intensity, which can be directly associated with holographic interferences. The CNNs employed provide an accurate and convenient ways to extract parameters, and represent a novel interpretational tool for strong-field ionization spectra.

Original languageEnglish
Article number083039
JournalNew Journal of Physics
Issue number8
StatePublished - 1 Aug 2023


  • convolutional neural networks
  • femtosecond pulse characterization
  • machine learning
  • strong-field ionization


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