  The Ornstein-Zernike (OZ) equation is the fundamental equation for pair
correlation function computations in the modern integral equation theory for
liquids. In this work, machine learning models, notably physics-informed neural
networks and physics-informed neural operator networks, are explored to solve
the OZ equation. The physics-informed machine learning models demonstrate great
accuracy and high efficiency in solving the forward and inverse OZ problems of
various bulk fluids. The results highlight the significant potential of
physics-informed machine learning for applications in thermodynamic state
theory.
