## 3 Model Complexity and Space Reduction Techniques for System-Level Optimization
### Surrogate Modeling
#### 3.1.3 Artificial Neural Networks  
Artificial Neural Networks (ANNs) are Machine Learning (ML)-based models that have been increasingly developed in recent years for the design and optimization of electrical machines, as they can significantly reduce the computational burden associated with FEM-based design processes [45; 46]. Their fundamental concept involves establishing a mapping between input and output parameters through a fitting process. They consist of the following three layers, as illustrated in Figure 8: input, output, and hidden. The variables \(x\) and \(y\) are the input and output values, respectively. The accuracy of the model typically increases with the number of hidden layers; however, additional hidden layers may also lead to longer training times or overfitting. The accuracy can also be increased through model complexity and feature engineering [45; 47]. A widely used procedure for improving model accuracy is hyperparameter tuning, where the parameters constituting the ANN are optimized. This process can be carried out using various optimization techniques such as PSO and GA. The authors of [48] propose a hybrid approach that combines both methods to mitigate PSO's tendency to become trapped at the local minima while also accelerating convergence, addressing the typically slower performance of the GA. Architectures commonly used for electrical machine optimization include a Feedforward Neural Network (FNN), Backpropagation Neural Network (BPNN), Radial Basis Function Neural Network (RBFNN), and Generalized Regression Neural Network (GRNN) [49].  
The authors of [50] propose an optimization method for a high-power-density SRM drive, dividing the process into two stages. In the first stage, a static analysis is conducted to identify the parameters that yield the highest static torque. In the second stage, a dynamic analysis is performed on these parameters to optimize the average torque, torque ripple, and radial forces. This is achieved using a RBFNN as a surrogate model in combination with optimization algorithms, such as the GA, PSO, and Global Response Surface Method (GRSM). An FEA is conducted using ALTAIR software, with the model fitting performedeither with the RBFNN through ALTAIR HyperStudy or with an ANN via Python. The study concludes that the fastest method is an ANN combined with the GRSM. For the control optimization, the conduction angles are optimized using the GA, and the results indicate that, while the average torque and radial forces are improved, the torque ripple remains unchanged. Additionally, the study provides comparative observations suggesting that the GA offers inclusiveness at the expense of time, whereas PSO provides faster convergence with a broad range of solutions.  
As with the case of the RSM, as well as according to research conducted by the authors, there is limited literature regarding the use of neural networks in the SLDOM, with most studies focusing on component-level optimization instead. In [51; 52], the authors focus on optimizing the motor by employing neural network models such as the GRNN and Multilayer Perceptron Neural Network (MLPN), in combination with PSO and the Fly Optimization Algorithm (FOA), in order to reduce the computational time. For instance, in [53], the computational time for optimization is reduced to just half an hour and an improvement is observed in the critical motor parameters, such as average torque, torque ripple, and efficiency. Additionally, the use of these methods facilitates the simulation of non-linearities inherent in the SRM, making them ideal for further implementation in the SLDOM.