Score

The quality of each grid point is evaluated based on a score function, which plays the role of the objective function to be minimized in the parameter-optimization problem.

The default score function is a weighted root mean square difference (RMSD) between the estimated property values and their corresponding reference values,

\[s_{\text{RMSD}}(i, \mathbf{a}^{(k)}, \mathbf{w}, \mathbf{r}) = \sqrt{\frac{1}{\sum\limits_{p=1}^{N_P}w_p}\,\sum\limits_{p=1}^{N_P} w_{p} \left( a^{(k)}_{pi} - r_p\right)^2} \quad ,\]

where

  • the index \(i\) is the linear index of the grid point under evaluation;

  • the index \(p\) runs over the composite properties;

  • \(N_P\) is the number of composite properties;

  • \(\mathbf{w} = (w_1,\cdots,w_{N_P})\) are the weights of the properties (given in the input file);

  • \(\mathbf{r} = (r_1,\cdots,r_{N_P})\) are the reference values of the properties (given in the input file);

  • \(\mathbf{a}^{{(k)}} = (a_{pi}^{(k)})_{p}\) is the vector of surrogate-model-estimated values of the properties for the grid point \(i\).

For flexibility, one can define customized score functions by means of the customization API.