Machine-learning calibration of intense x-ray free-electron-laser pulses using Bayesian optimization

X-ray free-electron lasers (XFELs) have brought new ways to probe and manipulate atomic and molecular dynamics with unprecedented spatial and temporal resolutions. A quantitative comparison of experimental results with their simulated theoretical counterpart, however, generally requires a precise characterization of the spatial and temporal x-ray pulse profile, providing a nonuniform photon distribution. The determination of the pulse profile constitutes a major, yet inevitable, challenge. Here, we propose a calibration scheme for intense XFEL pulses utilizing a set of experimental charge-state distributions of light noble gas atoms at a series of pulse energies in combination with first-principles simulations of the underlying atomic x-ray multiphoton ionization dynamics. The calibration builds on Bayesian optimization, which is a powerful, machine-learning-based tool particularly well suited for computationally expensive numerical optimization. We demonstrate the presented scheme to calibrate the pulse duration as well as the spatial fluence distribution profile of XFEL pulses. Our proposed method can serve as a comprehensive tool for characterizing ultraintense and ultrafast x-ray pulses.