We note that the uncertainties in the 12mer interaction energies are large, mainly because different EANN fittings show significant amounts of global shifts (see Figure ) in PES, but the relative energies between different water clusters remain largely stable. Therefore, taking an average of different EANN fittings solve the global shift problem. The major source of error for the current model comes from the short-range part. The average error for the EANN fitting is about 0.5-1.0 kcal/mol for hexamers and 12mers, making the exact ranking of all the structures a challenging task. In future, it can be further refined The second virial coefficient B2 can be measured experimentally over a wide range of temperatures. As a quantity only related to dimer interactions, it serves as a good benchmark for the two-body terms.