  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.
