Equivariant learning of a transferable three-dimensional classical density functional

2026-08-13

AI Summary

This work addresses the longstanding challenge of efficiently constructing liquid density functionals applicable across diverse thermodynamic conditions, interfacial settings, and confinement environments. The authors propose a three-dimensional, transferable density functional learning framework that requires no explicit labels for free energy or chemical potential. By integrating equivariant neural networks with variational self-consistency constraints, the method directly learns the functional from equilibrium density field data alone, rigorously preserving spatial symmetries and thermodynamic consistency. For the first time, this approach achieves generalization across temperature, system size, and statistical ensembles, accurately predicting unseen macroscopic phenomena—including structure factors, equations of state, vapor–liquid coexistence, interfacial broadening, non-monotonic solvation forces in complex geometries, and adsorption behavior in bicontinuous helical pore channels—demonstrating exceptional accuracy and transferability.

Abstract

Liquids exhibit collective behavior that depends sensitively on thermodynamic conditions, interfaces and confinement, yet predicting each new state commonly requires a separate atomistic simulation. Classical density functional theory offers a reusable variational description, but its central excess free-energy functional is generally unknown, and learned approximations have largely remained restricted to planar or lower-dimensional settings. Here we show that this functional can be learned directly from fully three-dimensional equilibrium density fields while preserving spatial symmetry and variational consistency, without free-energy or chemical-potential labels. A single learned functional transfers across temperatures, system sizes and statistical ensembles, and recovers structure factors, the equation of state, liquid--vapor coexistence and interfacial broadening, none of which are used as training targets. Applied to complex three-dimensional geometries, it predicts the non-monotonic force associated with formation and rupture of a solvent-depleted bridge between colloids and adsorption in an interconnected gyroid pore. These results demonstrate that equilibrium density data can be converted into a transferable thermodynamic generator connecting microscopic liquid structure to response, phase behavior and collective phenomena.

Problem

• classical density functional theory
• equivariant learning
• transferable functional
• three-dimensional liquids
• collective phenomena

Innovation

• equivariant learning
• classical density functional theory
• transferable functional
• three-dimensional liquids
• variational consistency