Neural density functionals: Local learning and pair-correlation matching

Abstract

Recently Dijkman et al. (arXiv:2403.15007) proposed training classical neural density functionals via bulk pair-correlation matching. We show their method to be an efficient regularizer for neural functionals based on local learning of inhomogeneous one-body direct correlations [Sammüller et al., Proc. Natl. Acad. Sci. 120, e2312484120 (2023), 10.1073/pnas.2312484120]. While Dijkman et al. demonstrated pair-correlation matching of a global neural free energy functional, we argue in favor of local one-body learning for flexible neural modelling of the full Mermin-Evans density functional map. Using spatial localization gives access to accurate neural free energy functionals, including convolutional neural networks, that transcend the training box.

arXiv comment6 pages, 2 figures + supplementary material (7 pages, 6 figures)

References in corpus (29)

• Critical point and coexistence curve properties of the Lennard-Jones fluid: A finite-size scaling study
• Deep-Learning Density Functional Theory Hamiltonian for Efficient ab initio Electronic-Structure Calculation
• Density functional theory for hard-sphere mixtures: the White-Bear version Mark II
• Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics
• Machine learning and density functional theory
• Machine Learning the Physical Non-Local Exchange-Correlation Functional of Density-Functional Theory
• Computer simulation of fluid phase transitions
• 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
• Neural-network Kohn-Sham exchange-correlation potential and its out-of-training transferability
• Use the force! Reduced variance estimators for densities, radial distribution functions and local mobilities in molecular simulations
• Noether's Theorem in Statistical Mechanics
• Neural functional theory for inhomogeneous fluids: Fundamentals and applications
• A classical density functional from machine learning and a convolutional neural network
• Machine-learning free-energy functionals using density profiles from simulations
• Analytical classical density functionals from an equation learning network
• Density depletion and enhanced fluctuations in water near hydrophobic solutes: identifying the underlying physics
• Machine learning the derivative discontinuity of density-functional theory
• Perspective: How to overcome dynamical density functional theory
• Force density functional theory in- and out-of-equilibrium
• Machine learning of a density functional for anisotropic patchy particles
• Physics-constrained Bayesian inference of state functions in classical density-functional theory
• Understanding the physics of hydrophobic solvation
• Why neural functionals suit statistical mechanics
• Physics-informed Bayesian inference of external potentials in classical density-functional theory
• Comparative study of force-based classical density functional theory
• Universality in Driven and Equilibrium Hard Sphere Liquid Dynamics
• Bypassing the energy functional in density functional theory: Direct calculation of electronic energies from conditional probability densities
• Dynamic Decay and Superadiabatic Forces in the van Hove Dynamics of Bulk Hard Sphere Fluids

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