## 1 Introduction  
Electrical machines have been intensively used in recent years in the automotive industry for applications that require high efficiency and reliability, switching designers' focus to the development of robust high-performance electrical machines. The design process of an electrical motor is a complex task that needs to deal with the non-linearity caused by the saturation of the iron at high magnetic field strength and the multi-physical nature of the investigated system, as well as with requirements that may come into conflict. Conventionally, the design process follows a sequential process: firstly, the electromagnetic targets are satisfied, then the stress and thermal aspects are analysed, leaving the noise, vibration and harshness (NVH) characteristics at the end. This means that at the end of the design process, only limited changes could be made to improve the noise and vibration characteristics. At the same time, since the design process is a multi-physical problem, where different domains are involved, experts from distinct fields must interact and contribute to achieve a robust, optimal design. Therefore, the electrical machine development process is an iterative and computational expensive one. Moreover, the multi-physical nature of motor characteristics analysis requires a synergy between 2D FEAfor electromagnetic and losses analysis and 3D FEA for structural characteristics. Hence, the overall time is increased by using finite element (FE) analysis, that is time consuming and memory intensive, even when parallelization techniques are used. Traditionally, the process used to design a high-performance electrical machine is multi-objective machine optimisation [1,2]. The optimal design is obtained by automatically varying the geometric parameters within predefined limits, for imposed objectives and constraints. The design space exploration is conducted using optimisation algorithms [3], the designer having the freedom to choose the objectives, constraints and parameters discretisation, selected based on manufacturing capabilities. Various studies from the state of the art are focused on finding the optimal design of electrical machines. Due to economical reasons (e.g., high cost of rare-earth materials) and the need for high power densities, the cost optimisation procedure gained popularity in the latter years, the machine being optimised to met the requirements at the lowest cost [4]. Different motor topologies, including permanent magnet and synchronous reluctance machines, are analysed in order to select the best design at the lowest cost in [5], while in [6], a permanent magnet synchronous machine (PMSM) is optimised to met the performance and cost demands, with focus on high-volume mass production and its constraints. Another optimisation objective is presented in [7], where the torque ripple is optimised to obtain a high and smooth torque. Nevertheless, the computational cost of an optimisation loop can drastically increase when a large number of machine designs are analysed. This is caused by the FE-based simulations conducted to evaluate the performances of the machine designs. Despite their well-known accuracy, the simulations based on FE may limit the optimisation process, due to their high computational cost (simulation times may vary from several minutes to several hours or even days [8]). To overcome the discussed issues, fast models can be developed using machine learning models [9], reducing the computational burden in the design stage, as most of the computations are carried out in the model building phase. At the same time, several processes can be brought earlier in the design cycle. This way, the system's performances and sensitivities can be identified in the concept stage and the designer can decide if the desired targets are met. Machine learning models used for design, optimisation, fault detection and robustness evaluation have been among the main research interests in electrical machines field over the years.