Neural Network Modeling of Heavy-Quark Potential from Holography

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.