An example of the computational cost of MB-PIPNet approach is shown in Fig. , where the time of single MD step is plotted against the number of water molecules. R c is the atomic or monomeric environmental cutoff applied in different MLPs. As seen, the MB-PIPNet approach exhibits a linear relationship between computational time and the number of molecules. Furthermore, with environment cutoff R c = 6 Å, the MB-PIPNet model approaches the speed of q-TIP4P/F force field and significantly faster than both DeepMD and polarizable force field TTM3-F. This indicates that the ideal balance between first-principle accuracy and conventional force field-level speed can be achieved through the proposed MB-PIPNet method. Details can be found in reference 83 29