## 6 Conclusions  
This paper presents a multi-physical machine learning approach for multi-attribute performance prediction of electrical motors. For that, the full process of designing the electrical motor is brought in the early-design stage, where all the characteristics (electromagnetic, motor losses, modal analysis mode-shapes and natural frequency) can be evaluated and predicted by the designer. The multi-attribute model is constructed based on the data achieved by conducting a series of 2D electromagnetic and 3D structural FE analysis on a set of motor models generated by modifying the DOFs consisting in the geometrical parameters of a base parametric motor model. Three independent machine learning models are developed for each analysed physics, one for electromagnetic torque and back emf harmonics, one for motor losses and one for the structural targets (modes and natural frequencies). The tested methods are support vector regression (SVR), gradient  
Figure 11: Machine learning model vs. FEA computational efficiency factor.  
boosting regressor (GBR) and Gaussian process regressor (GPR) and were selected due to their capacity to predict discrete datasets. Moreover, their accuracy is tested for four training datasets, 250, 500, 750 and 1000 samples. The fitting capabilities of the regression models are individually analysed. Two types of key performance indicator (KPI) are used to measure the fitting capabilities: the coefficient of determination (\(R_{2}\)) and the mean squared error (MSE). The results show that the GPR algorithm applied on 1000 samples is the most suitable machine learning model to predict the electromagnetic torque and back electromotive force harmonics orders, its \(R^{2}\) scores being higher than 0.95, while the MSE is less than 5%. For structural targets, the regressor that is able to fit the data with the best scores is the GPR model with 250 samples, \(R^{2}\) score being 1 and MSE 0%. Regarding the ability of the machine learning models to predict the motor losses, the GPR 1000 samples machine learning model presents the best results, with \(R^{2}\) scores of 1 and MSE values of 9%. It was demonstrated that the multi-attribute machine learning model developed by combining the best models for each physics involved can provide accurate and significant reduction in computational time, compared with the classical FEA approach.  
Conceptualization, M.R.R., S.C. and F.C.; writing--original draft preparation, M.R.R.; writing--review and editing, S.C., F.C. and C.M.; supervision, S.C., F.C. and C.M. All authors have read and agreed to the published version of the manuscript.  
This paper was financially supported by the Project \"Entrepreneurial competences and excellence research in doctoral and postdoctoral programs--ANTREDOC\", project co-funded by the European Social Fund financing agreement No. 56437/24.07.2019. This research was partially supported by the project 38 PFE in the frame of the programme PDI-PFE-CDI 2021.  
Not applicable.  
The authors would like to thank [PERSON] from Siemens Industry Software NV, Leuven, Belgium, for the help with building the machine learning model.  
The authors declare no conflict of interest.