核饱和性质在中子星$f$模振荡频率上的印记：一种机器学习方法
The footprint of nuclear saturation properties on the neutron star $f$ mode oscillation frequencies: a machine learning approach
AI总结：
本研究在相对论平均场框架下，采用机器学习、主成分分析、随机森林特征重要性分析及符号回归等方法，探究中子星$f$模振荡频率与核饱和性质的关联，为探测中子星核心特征提供新方法。
摘要：
我们在核物质的相对论平均场（RMF）框架范围内，采用机器学习（ML）方法研究了中子星（NS）非径向$f$模振荡频率与相应核物质状态方程（EOS）之间的复杂关联。我们采用Walecka模型的两种不同参数化方案，即（1）含标量场非线性自相互作用的方案（NL）以及（2）密度依赖贝叶斯模型（DDB），针对$f$模频率与各类核饱和性质的关联开展了全面研究。通过多种解析方法与机器学习方法，$f$模频率与核饱和性质之间的相关性揭示了中子星的复杂本质，以及其作为研究极端物质态的宇宙实验室的潜力。我们利用DDB模型与NL模型的混合数据集开展了主成分分析（PCA），以区分状态方程不同组分对$f$模频率的相对重要性。此外，“随机森林特征重要性”分析也阐明了在不同中子星质量范围内，这些性质在决定$f$模频率方面的不同作用。符号回归搜索进一步支撑了我们的研究结果，得到了具有强皮尔逊系数与极小误差的高精度关系式。这些关系式为从中子星非径向$f$模振荡观测中探测中子星核心特征（如能量密度、压强和声速）提供了新的方法。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
