## 4 Conclusions  
Both finite element and experimental methods that are being used by researchers for the electric and magnetic fields evaluation are extensively time-consuming and expensive. This paper intends to propose an extremely fast and low-cost implementation method using AI methods based on neural networks. The cascade-forward neural network (CFNN) as the main ANN method of this paper demonstrated higher accuracy than the commonly used feed-forward neural network (FFNN). For the electric and magnetic fields estimation, the CFNN exhibited a reduction in RMSE by 56% and 5%, respectively, compared to the FFNNN. The other important findings can be expressed as follows:  
* The training time of both models did not exceed 10 s, while it can take some days for the experimental and FEM methods.  
Figure 10: RMSE distribution chart for 50 iterations for the magnetic field best model.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Reference** & **Method** & **Field** & **RMSE** & **R\({}^{2}\)** & **Relative Error** \\ \hline
[34] & MLPNN & Electric & - & - & 5.437–23.62\% \\  & & Magnetic & - & - & 3.255–11.5\% \\
[13] & MLPNN & Electric & 0.030855 & - & - \\  & & Magnetic & 0.02719 & - & - \\
[13] & GRNN & Electric & 0.053084 & - & - \\  & & Magnetic & 0.03666 & - & - \\
[20] & NFC & Electric & - & - & 8–135\% \\  & & Magnetic & - & - & 5–190\% \\
[36] & FFNN & Electric & 0.6172 & 0.9121 & - \\  & & Magnetic & 0.3602 & 0.9471 & - \\
[35] & FFNN & Electric & - & - & - \\  & & Magnetic & - & 0.709–0.988 & - \\
**Present paper** & **CFNN** & **Electric** & **0.001708** & **0.99995** & **0.01–3.281\%** \\  & & **Magnetic** & **0.0246** & **0.99920** & **0.05–5.87\%** \\ \hline \hline \end{tabular}
\end{table}
Table 9: Comparison of accuracy of the proposed model with other works.  
* The response times of both proposed models were less than 10 ms, even using a regular personal computer. Therefore, they are very suitable for real-time use.
* Although the CFNN models have more complex architecture, they had almost the same response time to the FFNN, with higher accuracy.  
It is worth noting that CFNN models are versatile and can handle various datasets in many engineering applications. These models have been developed for one layout and have very high accuracy for that layout. To reach similar accuracy for other layouts, the models can be retrained and updated with new datasets related to them.  
Conceptualization, M.Y.-A.; methodology, S.A.B., W.S. and M.Y.-A.; formal analysis, S.A.B. and M.Y.-A.; resources, W.S. and M.Y.-A.; data curation, S.A.B.; writing--original draft preparation, S.A.B. and M.Y.-A.; writing--review and editing, W.S. and M.Y.-A.; funding acquisition, M.Y.-A.; supervision, W.S. and M.Y.-A. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data availability StatementData are available on request due to restrictions, e.g., privacy or ethical reasons.  
For the purpose of open access, the author(s) has applied a Creative Commons Attribution (CC BY) license to any Author Accepted Manuscript version arising from this submission.  
The authors declare no conflict of interest.