Data-Driven Einstein-Dilaton Model for Pure Yang-Mills Thermodynamics and Glueball Spectrum

We develop a machine learning assisted holographic model that consistently describes both the equation of state and glueball spectrum of pure Yang-Mills theory, achieved through neural network reconstruction of Einstein-dilaton gravity. Our framework incorporates key non-perturbative constraints of lattice QCD data: the ground ($0^{++}$) and first-excited ($0^{++*}$) scalar glueball masses pins down the infrared (IR) geometry, while entropy density data anchors the ultraviolet (UV) behavior of the metric. A multi-stage neural network optimization then yields the full gravitational dual -- warp factor $A(z)$ and dilaton field $\Phi(z)$ -- that satisfies both spectroscopic and thermodynamic constraints. The resulting model accurately reproduces the deconfinement phase transition thermodynamics (pressure, energy density, trace anomaly) and predicts higher glueball excitations ($0^{++**}$, $0^{++***}$) consistent with available lattice calculations. This work establishes a new paradigm for data-driven holographic reconstruction, solving the long-standing challenge of unified description of confinement thermodynamics and spectroscopy.