Variation Free Density Functional Theory: Data-driven Stochastic Optimization.

Density functional theory (DFT) is an efficient instrument for describing a wide range of nanoscale phenomena: wetting transition, capillary condensation, adsorption, etc. In this paper, we suggest a method for obtaining the equilibrium fluid density in a nanopore using DFT without calculating the free energy variation -- Variation Free Density Functional Theory (VF-DFT). This technique can be used to explore fluids with a complex type of interactions, systems with additional constraints and to speed up calculations. The fluid density is represented as a decomposition over a limited set of basis functions in VF-DFT. To build basis functions, we applied principal component analysis (PCA). PCA is used to extract the main patterns of the fluid density in the nanopore. The decomposition coefficients of the fluid density by the basis are sought by stochastic optimization algorithms: genetic algorithm (GA), particle swarm optimization (PSO) to minimize the free energy of the system. In this work, two different fluids were studied: nitrogen at a temperature of 77.4 K and argon 87.3 K, at a pore of 3.6 nm, and the performance of optimization algorithms was compared. We also introduce the Hybrid Density Functional Theory (H-DFT) approach based on stochastic optimization methods and the classical Picard iteration method to find the equilibrium fluid density in the pore. The combination of this method helps to significantly speed up the calculations of equilibrium density in the system without losing quality of the solution.