## 6 Conclusions
Using the RBF, we established correlation relationships between these proxies and site-specific average \(A\)Fs, considering the variability in initial \(A\)Fs across the 3564 values for each soil type. Both the overall period range and specific short- and mid- to long-period ranges associated with the amplification factors \(\text{F}_{\text{a}}\), \(\text{F}_{\text{v}}\), and \(\text{F}_{\text{i}}\) were analyzed. Using 50% of the database for training and the remaining 50% for testing, the RBF results demonstrated a lower standard deviation of the error term (\(\varepsilon_{\text{RBF}}\)) for \(\text{F}_{\text{a}}\), \(\text{F}_{\text{v}}\), and \(\text{F}_{\text{i}}\), generally with a reduction in the standard deviation exceeding 61%, along with a strong coefficient of determination exceeding 91%. These findings highlight the effectiveness of the RBF neural network method in accurately predicting amplification factors. The main findings of this study will aid in enhancing site classification by establishing a physical relationship between the \(A\)F and site proxies. However, several recommendations regarding regulatory codes can be made:  
* The Inclusion of the Fundamental Frequency: The fundamental frequency (\(f_{0}\)) should be considered alongside the peak ground acceleration (\(PGA\)) and shear wave velocity (\(V_{s30}\)) to improve predictions of amplification factors. * The Distinction of Period Ranges: It is crucial to differentiate between amplification factors for short (\(\text{F}_{\text{a}}\)), medium (\(\text{F}_{\text{v}}\)), and long (\(\text{F}_{\text{i}}\)) period ranges. The long-period amplification (\(\text{F}_{\text{i}}\)) is particularly significant, often exceeding \(\text{F}_{\text{a}}\) and \(\text{F}_{\text{v}}\) values for soil profiles with low \(V_{s30}\) values, which typically correspond to site classes C, D, and E in Eurocode 8 (EC8) and site classes D and E in UBC/CNBC codes. Finally, we propose new equations for predicting the amplification factor across specific short-, mid-, and long-period ranges. It is important to acknowledge the limitations of this study, primarily related to the use of simplistic soil profiles (homogeneous, monolayer, and 1D) and basic degradation curves, specifically those used by [PERSON] et al. (1988) [PERSON] et al. (1988) for clay and [PERSON] (1970) [PERSON] et al. (1970) for sand. Adopting more recent degradation curves and realistic soil profiles and site geometry could yield more accurate and site-specific amplification factors. Nevertheless, this study provides straightforward and effective prediction equations for amplification factors, utilizing a limited number of parameters that could enhance current design codes. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app15073618/s1](https://www.mdpi.com/article/10.3390/app15073618/s1)]([https://www.mdpi.com/article/10.3390/app15073618/s1](https://www.mdpi.com/article/10.3390/app15073618/s1)). Conceptualization, A.B.S. ; Methodology, A.B.S. ; Validation, L.G. ; Investigation, A.B.S. ; Writing--original draft, A.B.S. ; Writing--review & editing, L.G. ; Funding acquisition, L.G. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was partially supported by the Ecole de technologie superieure, University of Quebec, 1100 Notre-Dame Ouest, Montreal, QC H3C 1K3, Canada: [[https://www.etsmtl.ca/](https://www.etsmtl.ca/)]([https://www.etsmtl.ca/](https://www.etsmtl.ca/)) and by the Fonds de recherche du Quebec: [[https://frq.gouv.qc.ca/](https://frq.gouv.qc.ca/)]([https://frq.gouv.qc.ca/](https://frq.gouv.qc.ca/)). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The original contributions presented in this study are included in the article/Supplementary Material. Further inquiries can be directed to the corresponding author.