  Using Multi-Layer Perceptrons (MLP) and Kolmogorov-Arnold Networks (KAN), we
construct a holographic model based on lattice QCD data for the heavy-quark
potential in the 2+1 system. The deformation factor $w(r)$ in the metric is
obtained using the two types of neural network. First, we numerically obtain
$w(r)$ using MLP, accurately reproducing the QCD results of the lattice, and
calculate the heavy quark potential at finite temperature and the chemical
potential. Subsequently, we employ KAN within the Andreev-Zakharov model for
validation purpose, which can analytically reconstruct $w(r)$, matching the
Andreev-Zakharov model exactly and confirming the validity of MLP. Finally, we
construct an analytical holographic model using KAN and study the heavy-quark
potential at finite temperature and chemical potential using the KAN-based
holographic model. This work demonstrates the potential of KAN to derive
analytical expressions for high-energy physics applications.
