  Understanding and control of Laser-driven Free Electron Lasers remain to be
difficult problems that require highly intensive experimental and theoretical
research. The gap between simulated and experimentally collected data might
complicate studies and interpretation of obtained results. In this work we
developed a deep learning based surrogate that could help to fill in this gap.
We introduce a surrogate model based on normalising flows for conditional
phase-space representation of electron clouds in a FEL beamline. Achieved
results let us discuss further benefits and limitations in exploitability of
the models to gain deeper understanding of fundamental processes within a
beamline.
