## 1 Introduction
They perform well across various applications, such as time series forecasting and image recognition. Additionally, techniques like regularization and optimization enhance their performance, improving accuracy and reducing the risk of overfitting. Overall, neural networks are powerful tools for generating reliable predictions in many fields [36; 37; 38; 39; 40; 41; 42; 43]. Consequently, the use of ANNs to identify the most prominent selections of site proxies and how they correlate to site amplification factors offers a recent perspective that can help fill the existing gap. This study aims to identify the most effective site parameters for predicting the site amplification of the seismic response at the free surface of a soil deposit. More specifically, it focuses on establishing relationships between the amplification factor of the spectral response and a limited set of site proxies that describe the characteristics of soil profiles based on predictions of selected ANN methods. To achieve this goal, this study examines the 1D nonlinear responses of monolayer soil profiles with varying thicknesses and shear wave velocities, situated above a semi-infinite bedrock layer, subject to different seismic records, with varying intensities and frequency contents. More specifically, a total of 324 soil profiles of sand and clay are analyzed, each represented by a single layer with depths varying from 5 to 200 m and a shear wave velocity ranging from 100 to 600 m/s, underlain by a bedrock layer with a shear wave velocity varying between 750 and 1500 m/s. The nonlinear site responses of these profiles to the vertical propagation of shear (S) waves are calculated, including responses at free surfaces, which are used to determine site amplification factors. Fourteen (14) input waveforms are selected based on the recent studies by [PERSON] et al. (2017) and [PERSON] (2023) [8; 35]. Each of the considered profiles is subjected to these fourteen input motions, normalized to eleven different _PGA_ levels: 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.75, 0.9, and 1.05 g. This approach allows for the calculation of the mean amplification for each _PGA_ value, covering all relevant seismic frequency ranges. In total, 3564 geometric average amplification factors for each soil type are derived (324 soil profiles \(\times\) 11 _PGA_s). Several methods exist to calculate ground response with nonlinear behaviour. Nonlinear time history analyses are the common method for investigating the dynamic nonlinear behaviour of structures but are less widely used for soils. They are typically conducted using models discretizing the space domain, such as finite element models. While these methods generally yield accurate results and can model complex problems, they can be time-consuming due to their step-by-step integration procedure in the time domain combined with the iterative process for achieving a direct representation of the nonlinear soil response [44]. Instead, engineers often resort to a viscoelastic equivalent linear model combined with an iterative process, called equivalent linear analysis, to obtain the nonlinear solution for soils. This method, which is typically more computationally efficient, yields satisfactory results for engineering applications, especially within the relevant frequency range and for simple and smooth nonlinear behaviour [44; 45; 46; 47; 48; 49]. [PERSON] and [PERSON] (2015) have shown that nonlinear calculations of soil responses provided only slight performance improvements over equivalent linear methods while demanding considerably more time and complexity [47]. Consequently, given the large number of analyses to carry out (about 100,000), the equivalent linear approach is adopted in this study for efficiency. Furthermore, numerical methods, based on the finite element method, can solve one-, two-, and three-dimensional nonlinear soil problems, where amplifications can differ significantly from 1D scenarios, especially in the presence of valleys or rugged topography.