Training virial from forces and energys without raw virial datas

[ald3hyde]

Dear all,
I will try training NpT simulation to reproduce density, young modules, and etc. However, I don't have virial data, so I want to know how to calculate virials from forces, energies, and lattice parameters to fit the model with virial. Also, is the thermal effect included in the virial which DeepMD uses? I do not want to regenerate DFT data and would like to know your suggestions.

[njzjz]

The virial is defined in R. Clausius, Phil. Mag. 40, 122-127 (1870). You can also refer to the references of DeePMD-kit Comput. Phys. Comm. 228, 178-184 (2018) and J. Chem. Phys. 159, 054801 (2023), which contain the definition of virial.