Fig. 1: Experimental schematic and principle of Bayesian optimization algorithm.

a Schematic of the laser-plasma accelerator showing an ultrashort, intense laser pulse focused into a plasma source. The laser drives a relativistic plasma wave, accelerating electrons to MeV energies and producing keV X-rays. The spectral and spatial phase of the laser pulse prior to focusing, and density and length of the plasma source could all be controlled programatically. The electrons and X-rays were diagnosed by a permanent-dipole magnet spectrometer and a direct-detection X-ray camera, respectively. b–e 1D example of Bayesian optimization algorithm with n = 0, 1, 9, and 15 measured data points. The dashed red line represents the true function, the black line represents the surrogate model and the grey shaded region denotes the standard deviation of the model. Data points are sampled from the true function with some simulated measurement error (red circles). As more data points are added, the surrogate model begins to more closely resemble the true function. The blue line represents the acquisition function, the maximum of which tells the algorithm which point to sample next.