## 1 Introduction
Some works have already focused on generating machine learning models that allow replacement of the time consuming FEA and reduce the computational time. In [10], a statistical analysis that uses multiple correlation coefficients has been used to generate a fast model that is able to replace the FE model and reduce the computational effort, whereas in [11], the same objective is accomplished by using an artificial neural network. Another approach that uses online learning and dynamic weighting methods is presented in [12]. Moreover, in [3] the focus is on analyzing the effectiveness of using electrical machine machine learning models that incorporate tolerance or sensitivity aspects in a multi-objective optimization run. Further works focusing on machine-learning-assisted multi-objective optimisation are presented in [13], and in [14]. A recent work presents a data-driven structural modelling for electrical machine airborne vibration that is intended to be used in both design stage for optimisation purposes and in system-level simulations [15]. In [16], a multi-physics simulation workflow, based on reduce-order models, used to predict the vibro-acoustic behaviour of electrical and decrease the computation time is presented. The influence of the production mass tolerances modeled at system level and the interaction between the uncertainties and the drive's components, together with the fitted machine learning can be found in [1]. Fast prediction of electromagnetic torque and flux linkages used in system-level simulations are accomplished using a machine learning electromagnetic model based on artificial neural networks in [17]. Machine learning models employed to predict sound pressure levels are developed in [18,19], where it is proven that the developed models can be considered as replacements of the FEA for future design and optimization problems of the same motor. However, none of the above examples focus on the multi-physical characteristics of electrical machines, but only on the prediction of one physics (e.g., electromagnetic, thermal or structural characteristics). In [20], a data-aided, deep learning meta-model, based on cross-section image processing, is created to predict the multi-physical characteristics (e.g., maximum torque, critical field strength, costs of active parts, sound power) quickly and to accelerate the full optimisation process. The accuracy of this method is highly dependent on the chosen hyper-parameters settings and on the precision of the input data. Even if the hyper-parameters can be selected based on a sensitivity analysis, the accuracy is still dependent on the precision of input data. The image-based proposed method performs close to parameter-based method, that will be presented in this paper, only for increased pixel resolution of the training data, meaning that the method proposed in the cited work is memory intensive. This paper proposes to use geometric parametric models to evaluate the multi-physical performances of electrical machines and build a multi-attribute machine learning model. The aim is to characterise the development process of a multi-attribute machine learning model that is able to predict the multi-physical characteristics of electrical machines. The obtained machine learning model is capable to quickly and accurately estimate the multi-attribute performance from geometrical parameters (which represent the input data). At the same time, the model is suitable for inclusion in optimisation routines to reduce the process time and in system-level simulations for fast predictions. The main difference between the presented machine learning model and the ones found in the literature is the multi-physical feature of the developed model. The model can accurately estimate the torque and back electromotive force, motor losses and natural frequencies of the mode-shapes. Moreover, this article presents a way to simplify the machine learning problem by using a harmonic model to predict the electromagnetic values, reducing the computational burden in the training phase.