When it comes to the LIQWAT dataset which contains atomic coordinates and supercell dipole moments, the performance increase is approximately a factor of four for all the models when transitioning from PiNet to PiNet2, as shown in Table . This is likely to do with the LIQWAT dataset which samples a large conformational space. Table further shows that all models in the PiNet2-dipole family have a similarly good performance except for the BC(R) model. Molecular dipole moment in polar liquids is in an interesting quantity to study, because its magnitude and variation are directly linked to the dielectric properties of the polar liquid, and to the intensities in infrared spectroscopy. Previously, it was shown that the molecular dipole moment distribution inferred by the AC model with PiNet-dipole exhibited an excellent correlation with the Wannier dipole resolved from the maximally localized Wannier functions, despite that the AC model was not trained on this at all. This further illustrates the physical soundness of inferring atomic charges from the dipole moment prediction. The corresponding IR spectra predicted with PiNet2-dipole. The MLP-based MD simulations were generated using PiNet2-P3/revPBE0-D3 at 300 K and 0.996 g/cm 3 , see Section 4.5 for details. The experimental spectrum and that from DFTMD simulations (RevPBE0-D3 classical) 52 are also shown. The difference in the O-H stretching region was attributed to the nuclear quantum effects. Here, we have repeated this exercise for PiNet2dipole as well. Fig. shows that the PiNet2dipole/AC model predicts a molecular dipole moment distribution that corresponds well with the Wannier dipole distribution. This correlation improves when an AD contribution is added to the model for the AC+AD model. The AD and AD(OS) model also show a good correlation with the Wannier center distribution as shown in Fig. , but one that is slightly worse than that of the AC-type models. These suggest that a high correlation between ML-inferred molecule dipole and the Wannier dipole, regardless of the architectures and the models, is not coincidence.