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We have constructed deep neural networks, which can map fluctuatingphoto-electron spectra obtained from noisy pulses to spectra from noise-freepulses. The network is trained on spectra from noisy pulses in combination withrandom Hamilton matrices, representing systems which could exist but do notnecessarily exist. In [Giri et al., Phys. Rev. Lett. 124,113201 (2020)] weperformed a purification of fluctuating spectra, that is mapping them to thosefrom Fourier-limited Gaussian pulses. Here, we investigate the performance ofsuch neural-network-based maps for predicting spectra of double pulses, pulseswith a chirp and even partially-coherent pulses pulses from fluctuating spectragenerated by noisy pulses. Secondly, we demonstrate that along with apurification of a fluctuating double-pulse spectrum, one can estimate thetime-delay of the underlying double pulse, an attractive feature forsingle-shot spectra from SASE FELs. We demonstrate our approach with resonanttwo-photon ionization, a non-linear process, sensitive to details of the laserpulse.

Perspectives for analyzing non-linear photo ionization spectra with deep neural networks trained with synthetic Hamilton matrices