## 1 Introduction
Specifically, the rotational velocity of the star can impact g-mode frequencies and their associated damping times. Rapid stellar rotation can precipitate mode coupling and frequency splitting, while intense magnetic fields may suppress or alter g-mode oscillations. Furthermore, neutrino emission can modify the thermal structure of the star, subsequently influencing the g-mode frequencies. The physical characteristics of the source make estimating the HFF slope crucial for conducting parameter estimation with CCSN GW signals. Throughout this paper, we focus on an emerging feature present in CCSN GW signals, specifically the HFF, a consistent signature present in all GW signals from CCSN numerical simulations [4; 6; 16; 21]. It can be recognizable in time-frequency representations as a continuous, linear feature, beginning at around 150 Hz and progressing to approximately \(\sim\)1-2 KHz over time. Estimation of this parameter could be used to provide physical information on the source of CCSN GW [27] and to be incorporated into studies relating different characteristics, such as Standing Accretion Shock Instabilities (SASI), which represent a series of hydrodynamic instabilities observed in the post-bounce stage of CCSN. These instabilities are vital in influencing the supernova explosion's dynamics and the shock wave's interaction as it travels through the collapsing star's outer layers. Theyhave been used, for example, in [28], to determine the initial timing of SASI in numerical simulations of CCSN GW signals. In this research, we assume that the detection of GW from a CCSN is established; in this context, we assume that a GW is embedded in a laser interferometric noisy observation. Our objective is to create a data analysis framework to estimate the slope of the HFF, which connects the observed characteristics of the signal in the time-frequency evolution to the physical processes occurring at the source. To estimate and study the slope of the HFF, we proceed as follows: (i) We produced stochastic signals with an analytical approach, where the slope of the HFF is determined using a simple geometric relationship in the spectrogram of the signal. Analytical signals mimic CCSN GW generated by numerical simulations, showing a linear evolution of the high-frequency content [5]. (ii) The LIGO interferometric noise of the scientific run O3b is combined with the analytical CCSN GW signals to generate observations of GW embedded in noise, and then the time-frequency response is computed. These time-frequency representations are then converted into a two-dimensional real matrix that captures the important physical details of the event, including the HFF slope. (iii) We use such numerical arrays to construct a data set that comprises the HFF slope values ranging from 500 Hz/s to 5000 Hz/s. (iv) We carried out a Monte Carlo simulation in which each iteration randomly divides the data set into two parts: 70% for training and 30% for testing. This partitioning is used to assess the performance of different machine learning (ML) regression models [29]. (v) The performance of each ML model for regression algorithm is evaluated using a collection of performance metrics, which are used to verify the choice of a specific ML method [30]. The methodology described previously is illustrated in Figure 1.  
We present a comprehensive study that involves the implementation of various linear regression algorithms [31], including Linear, Ridge, LASSO, Bayesian Ridge, along with Decision Trees, and Deep Neural Networks [20], to estimate the slope of the HFF. This manuscript is organized as follows. Section 2 describes the construction of the data set. In Section 3, we present the algorithms and metrics used to define the properties of the data set. In Section 4, the results of the implementation and the accuracy of each  
Figure 1: Illustration of the methodology implemented in this paper. We generated a data set using CCSN GW signals with known HFF slope.