  Recent years have seen a significant increase in the use of machine
intelligence for predicting electronic structure, molecular force fields, and
the physicochemical properties of various condensed systems. However,
substantial challenges remain in developing a comprehensive framework capable
of handling a wide range of atomic compositions and thermodynamic conditions.
This perspective discusses potential future developments in liquid-state
theories leveraging on recent advancements of functional machine learning. By
harnessing the strengths of theoretical analysis and machine learning
techniques including surrogate models, dimension reduction and uncertainty
quantification, we envision that liquid-state theories will gain significant
improvements in accuracy, scalability and computational efficiency, enabling
their broader applications across diverse materials and chemical systems.
