shown in Figure show how many of the screened thermodynamic observables are controlled in these simplified water models by the water dipole (µ), which is a composite variable that depends on both the charge (q) and geometry (d) of the water model (µ = qd). This leads to an inherent indeterminacy in the solutions that are systematically obtained. This means that different combinations of charge and size can correspond to equally optimal solutions toward the fitting of the targeted properties. A set of optimal solutions is thus typically obtained in such automatic optimizations instead of a single specific one. The PCA data of Figure show how all such obtained "optimal" solutions belong, in our case, to the same global highdensity minimum. In Figures it is demonstrated how all the slightly different solutions belonging to such minimum represents share nearly identical molecular dipole and enthalpy of vaporization. While the broadness of such minima could be interpreted, e.g., as to be imputable to some kind of statistical error/limit in the particle swarm optimization method used herein, these results suggest that this is most likely related to an intrinsic indeterminacy in how the problem is posed. In particular, the degrees of freedom in such "coarse-grained" atomistic description of the water models are so limited that the optimization process degenerates, providing equally optimal solutions that are nonetheless different from each other.