Determining the Chemical Potential via Universal Density Functional Learning.

Area of Science:

• Computational physics
• Machine learning
• Soft matter physics

Background:

• Determining chemical potential in inhomogeneous classical fluids is computationally challenging.
• Traditional methods for chemical potential measurement are often inefficient.
• Density functional theory (DFT) is a powerful tool for studying many-body systems.

Purpose of the Study:

• To develop a machine learning approach for simultaneously determining equilibrium chemical potential and density functionals.
• To provide an efficient alternative to conventional computational techniques for chemical potential measurement.
• To enable the construction of neural density functionals from simulation data for accurate multiscale predictions.

Main Methods:

• Machine learning applied to density functionals.
• Minimization of a loss function derived from an Euler-Lagrange equation.
• Local representation of the universal one-body direct correlation functional using a neural network.
• Utilizing data from Brownian dynamics, molecular dynamics, or Monte Carlo simulations.

Main Results:

• Simultaneous determination of equilibrium chemical potential across simulation datasets.
• Successful representation of the universal one-body direct correlation functional by a neural network.
• Identification of system-specific unknown chemical potential values.
• Demonstration of an efficient alternative to conventional chemical potential measurement techniques.

Conclusions:

• Machine learning of density functionals provides an efficient and accurate method for determining chemical potential in classical fluids.
• The developed approach facilitates the construction of neural density functionals for multiscale predictions of soft matter systems.
• This method integrates simulation data with machine learning for advancing computational physics and materials science.