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This paper presents a novel approach to improve the accuracy of classical density functional theory (cDFT) by incorporating machine learning. The authors use a physics-informed learning framework to augment cDFT with neural network corrections, trained against molecular dynamics data. This method preserves thermodynamic consistency while capturing missing correlations, leading to improved predictions of interfacial thermodynamics across scales. The significance lies in its potential to improve the accuracy of simulations and bridge the gap between molecular and continuum scales, which is a key challenge in computational science.
Reference

The resulting augmented excess free-energy functional quantitatively reproduces equilibrium density profiles, coexistence curves, and surface tensions across a broad temperature range, and accurately predicts contact angles and droplet shapes far beyond the training regime.