Learning Neural Free-Energy Functionals with Pair-Correlation Matching
arxiv(2024)
摘要
The intrinsic Helmholtz free-energy functional, the centerpiece of classical
density functional theory (cDFT), is at best only known approximately for 3D
systems, which hampers the use of cDFT as a powerful tool for describing the
intricate thermodynamic equilibrium properties and structural aspects of
classical many-body systems. Here we introduce a method for learning a
quasi-exact neural-network approximation of this functional by exclusively
training on a dataset of radial distribution functions. This method based on
pair-correlation matching circumvents the need to sample costly heterogeneous
density profiles in a wide variety of external potentials and hence offers a
pathway to significantly ease the computational demands for future approaches
to extend machine learning for cDFT to arbitrary three-dimensional systems. For
a supercritical 3D Lennard-Jones system we demonstrate that the learned neural
free-energy functional accurately predicts planar inhomogeneous density
profiles under various complex external potentials obtained from simulations,
while simultaneously offering precise thermodynamic predictions far outside the
training regime.
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