## 5 Conclusions  
This research highlights the considerable promise of symbolic regression (SR) in the context of Wireless Power Transfer (WPT) systems, achieving accuracy levels on par with neural networks (NNs). SR emerges as a powerful method for extracting analytical expressions that model intricate relationships within WPT systems, providing both high predictive precision and interpretability. The methodology has demonstrated a notable degree of universality, evidenced by its successful application across three distinct scenarios. Firstly, it accurately predicted the distance in a Near-Field Communication Wireless Power Transfer (NFC-WPT) system using simulated data and S-parameters as input. Secondly, it achieved similar predictive accuracy for distance in an NFC-WPT system utilizing experimental data and Z-parameters. Finally, the method effectively predicted phase in an inductive WPT coil, even with highly irregular experimental data and frequency as the input. In all three cases, accurate predictive outcomes were obtained, supporting the assertion of its broad applicability. Future investigations will extend the validation of this SR method to encompass more complex WPT systems, such as the moving WPT system like in [47] and with a more complex structure of the WPT system, such as an array of receiver coils as in [48], thereby rigorously assessing the generalizability of the SR method on WPT systems. Nonetheless, additional studies are needed to optimize its performance by narrowing the search space through the integration of physical constraints and symmetries, such as the radial symmetry present in coil designs. These adjustments could enhance the efficiency and accuracy of SR models while lowering computational demands. Although this study concentrates on applying SR to predict the distance between coils and the phase-frequency relationship, its utility extends to other aspects of WPT systems. For instance, SR could be used to predict key properties like coupling coefficient or mutual inductance as a function of system parameters [49]. The sensitivity of SR models to errors, particularly noise and uncertainties, necessitates a rigorous analysis for future applications in WPT systems, especially when compared to the robustness of neural networks. As highlighted in [50], tolerance analysis is crucial for accurately assessing interoperability in wireless charging systems, as manufacturing tolerances and parameter drift can significantly impact test results and lead to misjudgments, necessitating the establishment of clear tolerance zones to ensure precise classification. Unlike conventional linear regression methods, which depend on approximations and manual calculations, SR can autonomously generate more precise results. By automating the identification of exact mathematical relationships, SR has the potential to simplify the design and optimization processes in WPT systems. In summary, SR offers a promising direction for advancing WPT research and technology. Its capacity to merge the advantages of machine learning with analytical modeling positions it as a versatile tool for tackling complex issues in this field. Future efforts should aim to broaden its applications within WPT systems and investigate methods to further enhance its efficiency and reliability. This could lead to the development of more innovative and effective Wireless Power Transfer solutions.  
Conceptualization, D.M., L.S., R.A. and F.R.F.; methodology, D.M., L.S., R.A. and F.R.F.; validation, D.M., L.S., R.A. and F.R.F.; writing--original draft preparation, D.M., L.S., R.A. and F.R.F.; writing--review and editing, D.M., L.S., R.A. and F.R.F.; supervision, F.R.F. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors upon request.  
The authors declare no conflicts of interest.