Why neural functionals suit statistical mechanics

Abstract

We describe recent progress in the statistical mechanical description of many-body systems via machine learning combined with concepts from density functional theory and many-body simulations. We argue that the neural functional theory by Sammüller et al. [Proc. Nat. Acad. Sci. 120, e2312484120 (2023)] gives a functional representation of direct correlations and of thermodynamics that allows for thorough quality control and consistency checking of the involved methods of artificial intelligence. Addressing a prototypical system we here present a pedagogical application to hard core particle in one spatial dimension, where Percus' exact solution for the free energy functional provides an unambiguous reference. A corresponding standalone numerical tutorial that demonstrates the neural functional concepts together with the underlying fundamentals of Monte Carlo simulations, classical density functional theory, machine learning, and differential programming is available online at https://github.com/sfalmo/NeuralDFT-Tutorial.

25 pages, 7 figures, 170 references; for associated online tutorial, see: https://github.com/sfalmo/NeuralDFT-Tutorial

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Cited by in corpus (15)

• Hyper-density functional theory of soft matter
• 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
• Why hyperdensity functionals describe any equilibrium observable
• Noether invariance theory for the equilibrium force structure of soft matter
• Metadensity functional theory for classical fluids: Extracting the pair potential
• Learning the bulk and interfacial physics of liquid-liquid phase separation with neural density functionals
• Neural Density Functional Theory in Higher Dimensions with Convolutional Layers
• Why gauge invariance applies to statistical mechanics
• Gauge invariance and hyperforce correlation theory for equilibrium fluid mixtures
• Determining the chemical potential via universal density functional learning
• Metadensity functional learning for classical fluids: Regularizing with pair correlations
• Confusion-driven machine learning of structural phases of a flexible, magnetic Stockmayer polymer
• Routes to the density profile and structural inconsistency