The neural network training was performed with the Pytorch 2.1.2 deep learning library 108 . The input features (Sec. S5 in the SI) were obtained in Python from the HF PySCF output of the given chemical system and pointwise evaluated on the DFT grid 107 . In particular, two FOD features at electronic temperatures T 1 = 10000K and T 2 = 25000K were employed for every system. Their implementation is based on the formula from Ref. 73, which we normalize by the density to obtain a dimensionless quantity. We employed the Adam optimizer 109 in Pytorch for NN training with custom learning rates incorporating a warm-up period and a fixed number of training steps (epochs).