The molecular charges and molecular dipoles computed from the ML predicted partial atomic charges agree well with the results from the QM Iterative Hirshfeld charges, as shown in Fig. . The R 2 values for the test set are around 0.9. The water molecular charge ranges (2.305 D), and close to the experimental estimate of the average molecular dipole for liquid water(∼2.9 D ). It is evident that the effects of charge transfer and polarization predicted from the QM/MM calculations are well captured by our KRR ML model. However, our ML model has a shortcoming: it does not guarantee the overall neutrality of the simulation system since no global charge constraint is imposed in our model. To remedy this issue, following the correction scheme in Ref. 23, we corrected the partial atomic charges predicted from ML to ensure a neutral simulation system. In our calculations, the charge correction was very small, typically around 0.001 (0.0005) for oxygen (hydrogen), and the corrected charges, q i , were used for all the property calculations in this work.