ArticleProceedings of the National Academy of Sciences of the United States of America2023
Neural functional theory for inhomogeneous fluids: Fundamentals and applications.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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Who cites it
7 citing papers in PubMed.
- A unified machine-learning framework for ab initio multiscale modeling of liquids.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- Ferroelectricity in Dipolar Liquids: The Role of Annealed Positional Disorder.The journal of physical chemistry. B · 2026Article
- Metadensity Functional Learning for Classical Fluids: Regularizing with Pair Correlations.The journal of physical chemistry. B · 2026Article
- Roles of Bulk and Surface Thermodynamics in the Selective Adsorption of a Confined Azeotropic Mixture.The journal of physical chemistry. B · 2026Article
- Synergizing Chemical and AI Communities for Advancing Laboratories of the Future.ACS central science · 2026Review
- Dielectrocapillarity for exquisite control of fluids.Nature communications · 2026Article
- Neural functional theory for inhomogeneous fluids: Fundamentals and applications.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
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4 authors.
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Abstract
We present a hybrid scheme based on classical density functional theory and machine learning for determining the equilibrium structure and thermodynamics of inhomogeneous fluids. The exact functional map from the density profile to the one-body direct correlation function is represented locally by a deep neural network. We substantiate the general framework for the hard sphere fluid and use grand canonical Monte Carlo simulation data of systems in randomized external environments during training and as reference. Functional calculus is implemented on the basis of the neural network to access higher-order correlation functions via automatic differentiation and the free energy via functional line integration. Thermal Noether sum rules are validated explicitly. We demonstrate the use of the neural functional in the self-consistent calculation of density profiles. The results outperform those from state-of-the-art fundamental measure density functional theory. The low cost of solving an associated Euler-Lagrange equation allows to bridge the gap from the system size of the original training data to macroscopic predictions upon maintaining near-simulation microscopic precision. These results establish the machine learning of functionals as an effective tool in the multiscale description of soft matter.
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