标题： 核饱和性质对中子星 $f$ 模态振荡频率的影响：一种机器学习方法 显示英文标题

标题： The footprint of nuclear saturation properties on the neutron star $f$ mode oscillation frequencies: a machine learning approach

摘要： 我们利用机器学习方法，在相对论平均场框架下研究了中子星（NS）的非径向\(f\)模态振荡频率与相应的核物质状态方程（EOS）之间的复杂关系。 使用瓦莱斯卡模型的两种不同参数化方法，即：(1) 标量场的非线性自相互作用（NL），以及 (2) 密度相关的贝叶斯模型（DDB），我们对\(f\)模态频率与各种核饱和性质之间的关系进行了全面分析。 通过多种解析和机器学习方法，\(f\)模态频率与核饱和性质之间的相关性揭示了中子星复杂性质及其作为极端物态宇宙实验室的潜力。 我们使用来自 DDB 和 NL 模型的混合数据集进行了主成分分析（PCA），以区分 EOS 各组成部分对$f$模态频率的重要性。 此外，{\it 随机森林特征重要性}分析还阐明了这些性质在决定\(f\)模态频率方面所起的不同作用，适用于一系列中子星质量范围。 我们的发现进一步得到了符号回归搜索的支持，得到了具有强皮尔逊系数和极小误差的高精度关系式。 这些关系式提出了探测中子星核心特性的新方法，例如从中子星非径向\(f\)模态振荡观测中推断能量密度、压力和声速等特性。 显示英文摘要

摘要： We investigate the intricate relationships between the non-radial \(f\) mode oscillation frequencies of neutron stars (NS)s and the corresponding nuclear matter equation of state (EOS) using a machine learning (ML) approach within the ambit of the relativistic mean field (RMF) framework for nuclear matter. With two distinct parameterizations of the Walecka model, namely, (1) with non-linear self interactions of the scalar field (NL) and, (2) a density dependent Bayesian model (DDB), we perform a thorough examination of the \(f\) mode frequency in relation to various nuclear saturation properties. The correlations between the \(f\) mode frequencies and nuclear saturation properties reveal, through various analytical and ML methods, the complex nature of NSs and their potential as the cosmic laboratory for studying extreme states of matter. A principal component analysis (PCA) has been performed using mixed datasets from DDB and NL models to discriminate the relative importance of the different components of the EOS on the $f$ mode frequencies. Additionally, a {\it Random forest feature importance} analysis also elucidates the distinct roles of these properties in determining the \(f\) mode frequency across a spectrum of NS masses. Our findings are further supported by symbolic regression searches, yielding high-accuracy relations with strong Pearson coefficients and minimal errors. These relations suggest new methodologies for probing NS core characteristics, such as energy density, pressure, and speed of sound from observations of non-radial \(f\) mode oscillations of NSs.