Metadensity functional learning for classical fluids: Regularizing with pair correlations

Abstract

We investigate and exploit consequences of the recent neural metadensity functional theory [Kampa et al., Phys. Rev. Lett. 134, 107301 (2025), 10.1103/PhysRevLett.134.107301] for describing the physics of inhomogeneous fluids. The metadensity dependence on the pair potential is relevant for soft matter design and Henderson inversion and it allows one to change the pair potential on the fly at prediction stage. Here we consider one-dimensional systems with short-ranged (truncated) interparticle forces and draw on the functional pair potential dependence to investigate 'metadirect' routes towards the bulk fluid pair correlation structure. Classical density functional theory provides the required functional relationships. Efficient variational calculus is implemented by neural functional line integration and automatic differentiation. We regularize local learning of neural functionals by comparing the pair structure from different routes. Thereby results from metadirect functional differentiation are matched against accurate test particle data from an initial locally trained metadensity functional. Accessing the pair structure via the metadensity functional dependence circumvents Ornstein-Zernike inversion and it is based on first principles.

16 pages, 5 figures

References in corpus (63)

• Towards self-driving laboratories: The central role of density functional theory in the AI age
• The van Hove distribution function for Brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics
• Inverse methods for design of soft materials
• Power functional theory for many-body dynamics
• A unified description of hydrophilic and superhydrophobic surfaces in terms of the wetting and drying transitions of liquids
• Dynamics in inhomogeneous liquids and glasses via the test particle limit
• The Local Compressibility of Liquids near Non-Adsorbing Substrates: A Useful Measure of Solvophobicity and Hydrophobicity?
• The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect
• Inverse Design for Self Assembly via On-the-Fly Optimization
• Noether's Theorem in Statistical Mechanics
• Neural functional theory for inhomogeneous fluids: Fundamentals and applications
• Non-negative Interfacial Tension in Phase-Separated Active Brownian Particles
• A classical density functional from machine learning and a convolutional neural network
• Superadiabatic forces in Brownian many-body dynamics
• Machine-learning free-energy functionals using density profiles from simulations
• Analytical classical density functionals from an equation learning network
• Velocity gradient power functional for Brownian dynamics
• Dielectric response with short-ranged electrostatics
• Density depletion and enhanced fluctuations in water near hydrophobic solutes: identifying the underlying physics
• Nonequilibrium phase behaviour from minimization of free power dissipation
• Flow and structure in nonequilibrium Brownian many-body systems
• Perspective: How to overcome dynamical density functional theory
• Structural nonequilibrium forces in driven colloidal systems
• Controlling the microstructure and phase behavior of confined soft colloids by active interaction switching
• Machine learning of a density functional for anisotropic patchy particles
• Understanding the physics of hydrophobic solvation
• Noether-Constrained Correlations in Equilibrium Liquids
• Physics-constrained Bayesian inference of state functions in classical density-functional theory
• Bulk dynamics of Brownian hard disks: Dynamical density functional theory versus experiments on two-dimensional colloidal hard spheres
• Reliable emulation of complex functionals by active learning with error control
• The phase behaviour and structure of a fluid confined between competing (solvophobic and solvophilic) walls
• Active interaction switching controls the dynamic heterogeneity of soft colloidal dispersions
• Fluctuation profiles in inhomogeneous fluids
• Relationship between Local Molecular Field Theory and Density Functional Theory for non-uniform liquids
• Learning classical density functionals for ionic fluids
• Structure and dynamics of responsive colloids with dynamical polydispersity
• Why neural functionals suit statistical mechanics
• Hyper-density functional theory of soft matter
• Physics-informed Bayesian inference of external potentials in classical density-functional theory
• Gauge Invariance of Equilibrium Statistical Mechanics
• Learning Neural Free-Energy Functionals with Pair-Correlation Matching
• Neural density functionals: Local learning and pair-correlation matching
• Bridging electronic and classical density-functional theory using universal machine-learned functional approximations
• Neural density functional theory of liquid-gas phase coexistence
• A classical density functional theory for solvation across length scales
• Bypassing the energy functional in density functional theory: Direct calculation of electronic energies from conditional probability densities
• Universality in Driven and Equilibrium Hard Sphere Liquid Dynamics
• Neural force functional for non-equilibrium many-body colloidal systems
• Dynamic Pair Correlations and Superadiabatic Forces in a Dense Brownian Liquid
• Why hyperdensity functionals describe any equilibrium observable
• Local measures of fluctuations in inhomogeneous liquids: Statistical mechanics and illustrative applications
• Metadensity functional theory for classical fluids: Extracting the pair potential
• Conditional probability density functional theory
• Learning the bulk and interfacial physics of liquid-liquid phase separation with neural density functionals
• Measures of Fluctuations for a Liquid Near Critical Drying
• Shear and bulk acceleration viscosities in simple fluids
• Dynamic Decay and Superadiabatic Forces in the van Hove Dynamics of Bulk Hard Sphere Fluids
• Neural Density Functional Theory in Higher Dimensions with Convolutional Layers
• Why gauge invariance applies to statistical mechanics
• Isometric and metamorphic operations on the space of local fundamental measures
• Dielectrocapillarity for exquisite control of fluids
• Determining the chemical potential via universal density functional learning
• The roles of bulk and surface thermodynamics in the selective adsorption of a confined azeotropic mixture