  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 molecular 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 confined fluids with a complex type of
interactions, additional constraints and to speed up calculations, which might
be crucial in an inverse problems. The fluid density in VF-DFT approach is
represented as a decomposition over a limited set of basis functions. We
applied Principal Component Analysis (PCA) to extract the basic patterns from
the density function and take them into account in the construction of a set of
basis functions. The decomposition coefficients of the fluid density by the
basis were 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 starting from the physically appropriate solution.
The combination of Picard iteration and stochastic algorithms helps to
significantly speed up the calculations of equilibrium density in the system
without losing the quality of the solution, especially in cases with the high
relative pressure and expressed layering structure.
