Validation loss (solid line) and training loss (dash-dot line) recorded during the NDE training, as a function of the cumulative epoch number for spectra compressed to 64 dimensions by the auto-encoder. The mathematical formulation of the loss function can be found in Greenberg et al. (2019); Deistler et al. (2022a). The flatness of the curves towards the end of the rounds indicates no significant overfitting and successful training of the NDE. Overfitting would appear as a sharp increase in validation loss, diverging from the training loss, signaling that the model tends to capture noise or overly complex patterns in the training data. The training time is indicated on the plot, where the largest value is found in the first inference round.