Deep neural networks trained with synthetic Hamilton matrices for non-linear photo-ionization spectra from fluctuating pulses

We construct 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 generated with noisy pulses and random Hamilton matrices, representing systems which could exist but do not necessarily exist. 

Such networks can "purify" fluctuating spectra, that is, map them to those from Fourier-limited Gaussian pulses [1]. Furthermore, the  neural-network-based maps can predict spectra of double pulses, pulses with a chirp and even partially-coherent pulses from fluctuating spectra generated by noisy pulses. Finally, we demonstrate that along with 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 [2]. We demonstrate our approach with resonant two-photon ionization, a non-linear process, sensitive to details of the laser pulse.