Toward a unified Einstein-Maxwell-dilaton framework of QCD

We propose HoloNet, a neural-network framework that unifies lattice QCD (LQCD) thermodynamics and holographic Einstein-Maxwell-Dilaton (EMD) theory within a data-to-holography pipeline. Instead of assuming specific functional forms, HoloNet learns the metric profile A ( z ) and the gauge-dilaton coupling f ( z ) directly from 2 + 1 -flavor LQCD data at μ = 0 . These learned functions are embedded into the EMD equations, enabling the model to reproduce the lattice equation of state and baryon number fluctuations with high fidelity. Once trained, HoloNet provides a fully data-driven holographic description of QCD that extends naturally to finite density, allowing us to map the phase diagram and estimate the location of the critical end point. The reconstructed potential V ( ϕ ) and coupling f ( ϕ ) agree quantitatively with those obtained from holographic renormalization, demonstrating that HoloNet can consistently bridge different holographic models.