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Photo-electron spectra obtained with intense pulses generated byfree-electron lasers through self-amplified spontaneous emission areintrinsically noisy and vary from shot to shot. We extract the purifiedspectrum, corresponding to a Fourier-limited pulse, with the help of a deepneural network. It is trained on a huge number of spectra, which was madepossible by an extremely efficient propagation of the Schr\"odinger equationwith synthetic Hamilton matrices and random realizations of fluctuating pulses.We show that the trained network is sufficiently generic such that it canpurify atomic or molecular spectra, dominated by resonant two- or three-photonionization, non-linear processes which are particularly sensitive to pulsefluctuations. This is possible without training on those systems.

Purifying electron spectra from noisy pulses with machine learning using synthetic Hamilton matrices