## 5 Machine Learning Model Computational Cost. Machine Learning Model versus FEA  
The purpose of developing the multi-attribute machine learning model is to reduce the computational time at the design stage and have a fast estimation of the motor performances, while maintaining the FEA high accuracy. This method allows an accurate  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Samples/**} & \multicolumn{2}{c}{**Tot**} & \multicolumn{2}{c}{**Wind**} & \multicolumn{2}{c}{**Iron**} & \multicolumn{2}{c}{**SBI**} & \multicolumn{2}{c}{**ST**} & \multicolumn{2}{c}{**RBI**} & \multicolumn{2}{c}{**Mag**} \\ \cline{2-13} \multicolumn{2}{c}{**Models**} & \(\mathbf{R^{2}}\) & **MSE** & \(\mathbf{R^{2}}\) & **MSE** & \(\mathbf{R^{2}}\) & **MSE** & \(\mathbf{R^{2}}\) & **MSE** & \(\mathbf{R^{2}}\) & **MSE** & \(\mathbf{R^{2}}\) & **MSE** \\ \hline \multirow{3}{*}{250} & SVR & 0.97 & 3 & 0.97 & 3 & 0.97 & 4 & 0.97 & 3 & 0.96 & 4 & 0.97 & 3 & 0.97 & 3 \\  & GBR & 0.87 & 13 & 0.94 & 5 & 0.9 & 10 & 0.87 & 12 & 0.92 & 8 & 0.88 & 11 & 0.87 & 13 \\  & GPR & 1 & 0 & 1 & 9 & 1 & 9 & 0.99 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ \hline \multirow{3}{*}{500} & SVR & 0.98 & 1 & 0.99 & 1 & 0.98 & 2 & 0.98 & 2 & 0.98 & 2 & 0.99 & 1 & 0.99 & 1 \\  & GBR & 0.92 & 8 & 0.96 & 4 & 0.93 & 7 & 0.9 & 9 & 0.94 & 6 & 0.93 & 6 & 0.92 & 8 \\  & GPR & 1 & 0 & 1 & 0 & 1 & 0 & 0.99 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ \hline \multirow{3}{*}{750} & SVR & 0.99 & 1 & 0.99 & 1 & 0.99 & 1 & 0.99 & 1 & 0.99 & 1 & 0.99 & 1 & 0.99 & 1 \\  & GBR & 0.93 & 6 & 0.97 & 3 & 0.95 & 5 & 0.93 & 7 & 0.96 & 4 & 0.94 & 6 & 0.94 & 6 \\  & GPR & 1 & 0 & 1 & 0 & 0.99 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ \hline \multirow{3}{*}{1000} & SVR & 1 & 0 & 1 & 0 & 1 & 0 & 0.99 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\  & GBR & 0.99 & 1 & 0.99 & 1 & 0.99 & 1 & 0.98 & 2 & 0.99 & 1 & 0.99 & 1 & 0.98 & 2 \\  & GPR & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Machine learning models performance to predict motor losses  
Figure 9: GPR 1000 samples accuracy. Predicted vs. original values for total motor, winding, iron, stator back iron, stator teeth, rotor back iron and magnets losses.  
system-level analysis and a fast optimisation routine. Therefore, an evaluation of the developed multi-attribute machine learning model capability to predict the optimal solution and its computational cost is performed. The multi-attribute machine learning model under test is defined by the combination of the best performance regressors for each physics involved, GPR 1000 for electromagnetic targets, GPR 250 for natural frequencies of modes and GPR 1000 for losses, and from now on denoted with ML1000.  
To quantify the advantage of using the ML1000 machine learning model over FEA, the model is included within a geometric optimization process that targets to maximise a function (e.g., natural frequency of a mode) with respect to imposed multi-physical constraints. In parallel, a FEA based optimisation procedure, having identical objectives and constraints to the ML1000 optimisation process, is performed on the structural and electromagnetic FE motor model. After that, the optimisation results of the two presented methods are compared from the point of view of accuracy and computational costs.