## 3 WPT System: Experimental and Simulated Data  
### WPT System Impedance  
The proposed method was evaluated using a near-field communication (NFC)-based WPT system operating at 13.56 MHz [40]. This system comprised two magnetically coupled planar resonators, facilitating power transfer between the transmitter and the receiver (Figure 1). A microcontroller, running a neural network (NN), adjusts the capacitance values of the circuit to achieve perfect impedance matching, thereby improving overall efficiency. The NN manages an AIMN made of an inductive-capacitance circuit consisting of three cascaded L-type lowpass stages in a series-series configuration (Figure 2). To obtain accurate impedance matching, the microcontroller adjusts three capacitance values of the ceramic capacitors labeled \(C_{1}\), \(C_{2}\), and \(C_{3}\). Based on those measurements, the microcontroller simultaneously measures the system's input impedance \((Z_{in})\) and the \begin{table}
\begin{tabular}{l c c c c} \hline
**NN Parameters** & **d** & **C** & **C from d** & **Frequency–Phase** \\ \hline INPUT data & S or Z & S or Z & S or Z and d & phase(0), f(0), R, z0 \\ \hline OUTPUT data & Distance & Capacitance & Capacitance & \(f_{goal}\) \\ \hline Dataset size & 57 & 57 & 57 & 18 \\ \hline Layers & 1 & 2 & 2 & 2 \\ \hline Neurons & 10 & 10, 10 & 10, 10 & 20, 10 \\ \hline Epochs & 100 & 1000 & 1000 & 500 \\ \hline Optimizer & trainlm & trainlm & trainlm & ADAM \\ \hline Activation function & sigmoid & sigmoid & sigmoid & ReLU \\ \hline Metrics and loss & MSE & MSE & MSE & MSE and MAE \\ \hline Learning rate & 0.1 & 0.05 & 0.1 & 0.001 \\ \hline Goal & \(3\times 10^{-5}\) & \(2\times 10^{-7}\) & \(2\times 10^{-7}\) & 0 \\ \hline Min grad & \(1\times 10^{-7}\) & \(1\times 10^{-7}\) & \(1\times 10^{-7}\) & Not specified \\ \hline Batch size & Not used & Not used & Not used & 4 \\ \hline Validation & Not used & Not used & Not used & 0.2 \\ \hline \end{tabular}
\end{table} 
Table 1: Neural network parameter summary. This table presents the key parameters employed in the experimental setups, facilitating reproducibility. Due to variations in implementation (MATLAB R2024b for Experiment 1; Python 3.11.11 for Experiment 2) and iterative model refinement, precise replication of all simulation results may be challenging. However, the listed parameters represent the foundational configurations. Experiment 1 utilized the trainlm optimizer, a backpropagation algorithm employing the Levenberg–Marquardt method. \(f_{goal}\) denotes the frequency at which the phase response falls below 5 degrees. The physical WPT is made of two circular coils, separated by a distance \(d\) and characterized by a mutual inductance \(k\). Transverse misalignment \((\Delta x)\) and \((\Delta y)\) and receiver coil rotation \((\theta)\) were introduced to simulate realistic operating conditions. The receiver was connected to a fixed load, while the transmitter was connected to both the microcontroller and the AIMN. Maximum power transfer was achieved through impedance matching via the AIMN. However, to mitigate potential AIMN-induced losses, the microcontroller was also programmed to bypass the AIMN when its activation was deemed detrimental. Here is the plot after the impedance matching performed by the AIMN, for the real and imaginary part of the input impedance, in Figure 7 and Figure 8, respectively. Figure 4: Imaginary part of impedance parameter with distance between the two coils, measured in the case 1, for no-misalignment between the two coils: \((\Delta x)\), \((\Delta y)\) and \((\theta)\) are zero. These measurements are taken for the WPT–NFC system from the side of the transmitter coil, before the impedance matching performed by the AIMN. Figure 5: Reflection scattering parameter, portl–portl measured from the transmitter side. Measurements are shown for different values of the distance between the two WPT coils, in the case 1 configurations, with \((\Delta x)\), \((\Delta y)\), and \((\theta)\) equal to zero.