Fig. 1: Schematic of the virtual spectrometer input and output sources, and of the different operational phases.

a Representative data from the grating spectrometer (blue solid line), which is used during the training phase (dashed line), and b time-of-flight data from the photo-electron spectrometer (dark green and orange lines), which is used during the training and inference (thick solid black line) phases. For the latter, only two out of sixteen channels are shown. Pulse energies provided by the x-ray gas monitor are employed during training and inference. c Representative data generated by the virtual spectrometer (red line), together with the 68% confidence level uncertainty band around the prediction (red band). d Selected region-of-interest of manually calibrated photo-electron spectrometer with energy axis on the top for each channel. Each channel has a different time-of-flight offset and independent calibration constants. e Comparison between grating spectrometer and virtual spectrometer in a selected region-of-interest. The Pearson correlation coefficient, ρ, between the GS and VS spectra can be seen in the plot.