## 2 Materials and Methods
### WPT System: Experimental and Simulated Data
#### 2.2.1 WPT NFC Impedance Matching
The ports shown are the ports used in the measurements of the scattering parameters and so also the impedance parameters. to predict the optimal values of \(C_{1}\), \(C_{2}\), and \(C_{3}\) required to achieve perfect impedance matching, based on the measured S-parameters or \(Z_{in}\). A NN with five hidden layers with 15 neurons each was used, trained using the Mean Square Error (MSE) as the loss function. However, analysis of the circuit with and without the AIMN revealed that, in some configurations, the additional circuit introduces losses and worsens the impedance matching performance. To address this, the microcontroller was also programmed to bypass the AIMN when its use was not advantageous. A substantial amount of data were collected from this system, including both experimental measurements and simulations. As for simulations, data were taken from different TX-RX locations to train, validate, and test the NN that controls the AIMN. This simulations were conducted on 229 different configurations, recreating the physical circuit in a simulation software, like SIMULINK (version R2024b) environment in Figure 1 or as performed by [41] using Cadence's AWR environment. In the simulations, various system configurations were considered, accounting for factors such as the distance between the two coils, misalignment, and the rotation angle of the receiver. This comprehensive dataset, which is available here [43], provides valuable insights into the behavior of the WPT system under different conditions. The dataset includes measurements of key parameters such as power transfer efficiency, impedance matching, and scattering parameters, enabling a detailed analysis of the system's performance. By leveraging these data, researchers can further refine the SR and NN models, improving their accuracy and applicability to real-world WPT systems. This approach not only enhances the understanding of WPT dynamics but also paves the way for the development of more efficient and reliable Wireless Power Transfer solutions. * Experimental data: 3 configurations are reported, in which \(\theta=0\), \(\Delta x=(0,\ 20,\ 30)\) mm, \(\Delta y=(0,\ 20,\ 25)\) mm. For each configuration, 57 points are measured at different distance values \(d\), with \(d\) going from 14 mm to 70 mm at 1 mm step. To reduce the noise, 5 measurements are taken at each position. The measured values are \(|S_{11}|\), \(|S_{21}|\), \(Z_{in}\) complex number and \(\Gamma\). Also, the capacitance values used for the perfect impedance matching are reported; the same measurements as mentioned above are taken after impedance matching performed by the AIMN. * Simulation data for comparison with experimental ones. The same configurations are considered but now the data are taken from the simulation. * Simulation data of 229 different configurations, with different \(\Delta x\), \(\Delta y\) and \(\theta\). For each of this configurations, there are 57 different points at different distance values. For each of them, the total complex matrix of the scattering parameters is reported, for 1001 points at different frequencies. To sum up, \(S\) parameters and \(Z_{in}\) parameters are measured from the experimental setup at 3 different configurations for 57 different distance values, while 229 configurations are simulated, always for 57 different distance values. The main focus of this article is to predict the distance values and the configuration of the system from the measured \(S\) parameters or \(Z_{in}\). Using symbolic regression would give not only good prediction but also analytical formulas that could be more efficient and faster to implement in a microcontroller to adapt the system to different configurations.