RSM Error Metrics

There are five error metrics available to assess the quality of a surrogate model in the Model tab of the Response Surface node. The commonly used metrics are defined below where \(r_i\) is taken to be the response of the actual (full) model and \(f_i\) is the response surface model evaluated at the \(i^\textrm{th}\) (input) sample index ranging. In the following definitions, \(i\) is simply taken to range from 1 to \(n\), however it should be noted that this range may be applied to either the complete dataset or the holdout data if cross-validation is being considered, see Model for more details.

Mean Squared Error

\[\textrm{MSE} = \frac{{1}}{{n}} {\sum_{i=1}^n \left(r_i - f_i \right)^2 }\]

Sum of Squared Error

\[\textrm{SSE} = {\sum_{i=1}^n \left(r_i - f_i \right)^2 }\]

R squared

\[\textrm{R}^2 = 1 - \frac{{\sum_{i=1}^n \left( r_i - f_i \right)^2}} {{\sum_{i=1}^n \left( r_i - \bar{r} \right)^2}}\]


\[\bar{r} = \frac{{1}}{{n}} {\sum_{i=1}^n r_i }\]

is the mean response.

L_infinity norm

\[\textrm{L}_\infty = \frac{{ \max \left| r_i - f_i \right| }}{{ \max \left| r_i \right| }}\]

L_1 norm

\[\textrm{L}_1 = \frac{{ \sum_{i=1}^n \left| r_i - f_i \right| }} {{ \sum_{i=1}^n \left| r_i \right| }}\]

L_2 norm

\[\textrm{L}_2 = \frac{{ \sum_{i=1}^n \left( r_i - f_i \right)^2 }} {{ \sum_{i=1}^n r_i^2 }}\]