How was the phase diagram of water developed?
Although many calculations can now be used, all of them originated with empirical (experimental) observations and correlations.
IUPAC has an excellent detailed history here: https://www.iupac.org/publications/pac/pdf/1999/pdf/7107x1183.pdf
The experiments are always necessary to refine and validate a theoretical equation. We use physical observations to see if our understanding of the underlying principles is, in fact, correct.
Even when we obtain useful equations for practical use, the actual physical reason for many of the equation factors is often still unknown.