Learning the bulk and interfacial physics of liquid-liquid phase separation with neural density functionals - Data and Models

This work is connected to the research detailed in the paper "Learning the bulk and interfacial physics of liquid-liquid phase separation" (to be published, Arxiv: https://arxiv.org/pdf/2507.08395) and the associated SWNeural software available on GitHub (https://github.com/SilasRobitschko/SWNeural)

Abstract: 

We use simulation-based supervised machine learning and classical density functional theory to investigate bulk and
interfacial phenomena associated with phase coexistence in binary mixtures. For a prototypical symmetrical Lennard-
Jones mixture our trained neural density functional yields accurate liquid-liquid and liquid-vapour binodals together
with predictions for the variation of the associated interfacial tensions across the entire fluid phase diagram. From the
latter we determine the contact angles at fluid-fluid interfaces along the line of triple-phase coexistence and confirm
there can be no wetting transition in this symmetrical mixture.

The dataset BinaryLJ_All_Runs.zip comprises 2200 Grand Canonical Monte Carlo (GCMC) simulation runs of a binary Lennard-Jones (LJ) fluid. The simulations were performed under a variety of random external potentials.

The primary purpose of this data is to serve as a training set for machine learning models aimed at deriving the c1-functional, a crucial component for classical density functional theory. 

The simulated system is a binary symmetric Lennard-Jones fluid with the following parameters: same-species interaction (ϵ11=ϵ22) and weakened cross-species interaction (ϵ12=0.7⋅ϵ11). The particle sizes are identical (σ1=σ2), and the potential is truncated at 2.5σ (without an energy shift being applied).

The data was generated using the MBD software package, developed by Florian Sammüller at the University of Bayreuth (https://gitlab.uni-bayreuth.de/bt306964/mbd).

Models_and_Results.zip includes two neural models trained on this dataset (as Pytorch-Path-Files) and their respective calculations of the Binodal of the aforementioned symmetric binary LJ fluid.  

Both models are basic fully connected neural models with the softplus activation function. 

The first original trained model has the following parameters: 
- Size: 1404x1024x512x512x512x2
- Learning Rate: 0.001
- Epochs: 100
- Decay/Epoch: 0.95

The refined model has the following parameters: 
- Size: 1404x512x512x512x512x2
- Learning Rate: 0.0003
- Epochs: 100
- Decay/Epoch: 0.90
- L2 Regularization: 1.0*10^-5