## 3 Simulation Results and Discussions  
### Artificial Neural Network Setup  
Different datasets with 10,000, 20,000, 40,000, and 100,000 samples were initially created in order to train the artificial neural networks. 90% of each dataset was used as training data, and the remaining 10% was used as test data to evaluate the performance of the neural network. Moreover, the training data were further divided into 90% training data, 5% test data, and 5% validation data. Initially, a set of 10,000 data samples was selected to evaluate the EDMnet architecture. According to the previous analysis, the \(EDMnet\) was configured with 42 neurons at the input layer and 6 neurons at the output layer. With the intention of determining the most appropriate ANN for this problem, a large number of simulations were performed, taking into account various parameters, i.e., the number of hidden layers, the number of neurons per layer, the type of training algorithm, the type of training transfer function at each layer, and various learning rates. Simulations were performed in a MATLAB environment using the NN toolbox. The optimal number of hidden layers was found to be four, with 580, 280, 180, and 80 neurons at each layer, respectively, and the most appropriate training algorithm was Resilient Backpropagation (trainrp). After testing all available transfer functions, the best results were obtained by applying the logistic sigmoid transfer function (logsig), which is expressed by f(x) = \(1/(1+\mathrm{e}^{-\mathrm{x}})\), to the first and fourth hidden layers. The normalized radial basis transfer function (radbasn) was selected for the second and third hidden layers. This is equivalent to radbasn given by f(x) = \(\mathrm{e}^{-\mathrm{x}/2}\), except that output vectors were normalized by dividing by the sum of the pre-normalized values [14]. Moreover, the linear transfer function was applied to the output layer. Also, simulations were performed for two learning  
Figure 2: (**a**) Setup of the 6 measurement points with an angle step of 60\({}^{\circ}\) and (**b**) setup of the 8 measurement points with an angle step of 45\({}^{\circ}\)[13]. rates (0.01, 0.001) and the best results were given by the learning rate \(LR=0.01\). In Figure 3 the neural network architecture is presented [6]. The performance during the training procedure for all neural network candidates was evaluated via the MSE (Mean Squared Error). At this point, it should be mentioned that the present problem had neural networks with multi-element outputs with different ranges. In order to avoid prioritizing the relative accuracy of the outputs with the larger range, the parameter 'normalization' of the MSE was set to 'percent'. By this adjustment, errors were normalized between \(-1\) and \(1\)[15]. A brief description of the methodology followed in this work is presented through the flow chart in Figure 4. In the left block, enclosed in the dashed lines, the steps followed from the measurement setup to the training data creation are depicted. Thus, initially, the 14 measurement points were defined and the equations of the electric field were formulated. Then, the size of the EUT (equipment under test) was determined, and based on this, the limits of the position of the electric dipole. At the same time, the appropriate boundaries of the electric moments \(\mathrm{p_{x}}\), \(\mathrm{p_{y}}\), and \(\mathrm{p_{z}}\) were selected. Hence, through the aforementioned steps, the artificial data were generated in a MATLAB R2022b environment. These data, as shown in the right block of the flow chart, were fed into neural networks, where the electric field values were the inputs and the six dipole parameters (x, y, z, \(\mathrm{p_{x}}\), \(\mathrm{p_{y}}\), \(\mathrm{p_{z}}\)) were the target outputs. Afterward, the necessary adjustments to the neural network were carried out, such as the selection of the appropriate training algorithm, the activation function, and the performance function.