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 $i^{\text{th}}$ (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

$$\text{MSE}=\frac{1}{n}\sum _{i=1}^n{(r_i-f_i)}^2$$

Sum of Squared Error

$$\text{SSE}=\sum _{i=1}^n{(r_i-f_i)}^2$$

R squared

$${\text{R}}^2=1-\frac{\sum _{i=1}^n{(r_i-f_i)}^2}{\sum _{i=1}^n{(r_i-\overline{r})}^2}$$

where

$$\overline{r}=\frac{1}{n}\sum _{i=1}^n{r}_i$$

is the mean response.

L_infinity norm

$${\text{L}}_{\mathrm{\infty }}=\frac{max|r_i-f_i|}{max\left|r_i\right|}$$

L_1 norm

$${\text{L}}_1=\frac{\sum _{i=1}^n|r_i-f_i|}{\sum _{i=1}^n\left|r_i\right|}$$

L_2 norm

$${\text{L}}_2=\frac{\sum _{i=1}^n{(r_i-f_i)}^2}{\sum _{i=1}^n{r}_i^2}$$