Equivariant learning of a transferable three-dimensional classical density functional

• URL: http://arxiv.org/abs/2608.13506v1
• Date: Thu, 13 Aug 2026 17:32:45 GMT
• Title: Equivariant learning of a transferable three-dimensional classical density functional
• Abstract summary: We show that classical density functional theory can be learned directly from fully three-dimensional equilibrium density fields.<n>A single learned functional transfers across temperatures, system sizes and statistical ensembles, and recovers structure factors.<n>It predicts the non-monotonic force associated with formation and rupture of a solvent-depleted bridge between colloids.
• Score: 0.1450405446885067
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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