Therefore, what we found here is that the EEMtype model powered by PiNet2-χ is now able to capture the correct physical scaling in polarizability for both conjugated and non-conjugated systems. When it comes to the actual performance beyond error metrics, it is found that the calculated O-O radial distribution functions (RDFs) obtained from PiNet and PiNet2-P3 are quite similar in the constant number of particles, volume and temperature (N V T ) ensemble. They also agree well with the experimental reference (Fig. ). However, things are quite different for the temperature-dependence of the density in the constant number of particle, pressure and temperature (N P T ) ensembles as shown in Fig. . The equilibrium densities were very much overestimated with PiNet while densities predicted from PiNet2-P3 agree surprisingly well with those reported by MACE. Therefore, it becomes clear that equivariant features play a critical role in MLPs for describing the structure and the thermodynamics of liquids and PiNet2-P3 appears to be very capable for describing this type of systems. Real electrolyte solutions contain ions, therefore, we have also tested the performance of PiNet2-P3 using the dataset that we call "NaCl(sol)-SCAN". This dataset 67 contains 26926 structures of NaCl aqueous solutions at a variety of concentrations, while the energy and force labels were obtained through DFT calculations with the SCAN functional. RM-SEs are 1.19 meV/atom for energy and 70 meV/ Å for force for PiNet2-P3, which are much smaller than the corresponding values obtained for PiNet, i.e. 2.17 meV/atom for energy and 126 meV/ Å. These number can be compared to the RMSEs of 0.3 meV/atom for energy and 72.4 meV/ Å from DeePMD in Ref. where the original dataset comes from.