Heavy quarkonium spectrum and decay constants from a neural-network-based holographic model

We present a data-driven inverse construction of the dilaton field in a bottom-up AdS/QCD description of heavy vector quarkonia. Instead of adopting an analytic ansatz, we use a multilayer perceptron to learn Φ ′ ( z ) as a smooth function of the holographic coordinate, with Φ ( 0 ) = 0 imposed to ensure ultraviolet consistency. The dilaton and its derivatives obtained by automatic differentiation generate the holographic potential U ( z ) , and the associated Schrödinger-like equation is discretized and diagonalized to extract the low-lying eigenmodes. Masses and decay constants are then evaluated from the eigenvalues and the near-boundary behavior of the bulk-to-boundary modes. Training on PDG data for charmonium and bottomonium yields a nonquadratic dilaton profile that resolves the long-standing difficulty of simultaneously reproducing both the heavy quarkonium spectrum and the monotonic suppression of leptonic decay constants with radial excitation. The combined fit achieves rms deviations of 1.26% (charmonium) and 3.32% (bottomonium). This work establishes neural-network reconstruction as a flexible tool for holographic modeling and provides a basis for future extensions incorporating additional channels, lattice constraints, or finite-temperature backgrounds.