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

We have constructed deep neural networks, which can map fluctuating photo-electron spectra obtained from noisy pulses to spectra from noise-free pulses. The network is trained on spectra from noisy pulses in combination with random Hamilton matrices, representing systems which could exist but do not necessarily exist. In [Giri et al., Phys. Rev. Lett. 124,113201 (2020)] we performed a purification of fluctuating spectra, that is mapping them to those from Fourier-limited Gaussian pulses. Here, we investigate the performance of such neural-network-based maps for predicting spectra of double pulses, pulses with a chirp and even partially-coherent pulses pulses from fluctuating spectra generated by noisy pulses. Secondly, we demonstrate that along with a purification of a fluctuating double-pulse spectrum, one can estimate the time-delay of the underlying double pulse, an attractive feature for single-shot spectra from SASE FELs. We demonstrate our approach with resonant two-photon ionization, a non-linear process, sensitive to details of the laser pulse.