Equivariant learning of a transferable three-dimensional classical density functional
2026-08-13 • Machine Learning
Machine Learning
AI summaryⓘ
The authors developed a way to teach computers to understand how liquids behave by learning from 3D snapshots of how molecules are spread out in space. This method doesn't need specific energy labels and works across different temperatures and sizes. It can predict important liquid properties like when liquid turns to vapor or how liquids act near surfaces and in complex shapes. Their approach helps connect tiny molecular details to big-picture liquid behaviors without running new simulations each time.
Classical density functional theoryExcess free-energy functionalEquilibrium density fieldsLiquid-vapor coexistenceStructure factorsEquation of stateInterfacial broadeningColloidsGyroid poreSolvent-depleted bridge
Authors
Bingqing Cheng
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.