Hyperdensity functional theory of soft matter

This repository contains code, data sets and models corresponding to the following publication:

Hyperdensity functional theory of soft matter
Florian Sammüller, Silas Robitschko, Sophie Hermann, and Matthias Schmidt, Phys. Rev. Lett. 133, 098201 (2024); arXiv:2403.07845.

For an introductory account and detailed derivations, see also:

Why hyperdensity functionals describe any equilibrium observable
Florian Sammüller and Matthias Schmidt, J. Phys.: Condens. Matter 37, 083001 (2025); arXiv:2410.10534.

Setup

A recent version of Julia must be installed on your system. Launch the Julia REPL and enter the package manager by typing ]. Set up the project as follows:

activate .
instantiate

Instructions

We consider the hard rod fluid ("HR"), the square well fluid with a range of 1.2 ("SW1.2") in one spatial dimension and the hard sphere fluid ("HS") in planar three dimensional geometry. To test the hyper-DFT framework, the non-trivial observable of interest is chosen to be the largest cluster size of a given microstate (see also simulation.jl for an algorithm to detect particle clusters).

Neural direct correlation functionals (see also NeuralDFT and NeuralDFT-Tutorial) can be loaded from the files model_<particles>.bson. Simulation data is provided in the directories data_<particles>_L<system length> (raw) and in the files data_<particles>_L<system length>.jld2 (preprocessed). The trained hyper-direct correlation functionals for the considered cluster observable are saved in the files model_cluster_<particles>_L<system length>.bson.

Code to generate and process the reference simulation data as well as to train the neural hyper-direct correlation functional is given in main.jl (the data for the 3D HS fluid has been generated with MBD). Utilities are provided in simulation.jl, dft.jl and neural.jl. Plots of the manuscript can be reproduced with plots.ipynb (start a Jupyter server to run this notebook).