Using Computational Intelligence for solving the Ornstein-Zernike equation

TL;DR

This paper explores using neural networks and evolutionary optimization to solve the Ornstein-Zernike equation for simple liquids, achieving results comparable to molecular simulations.

Contribution

It introduces neural network parametrization of closure relations and incorporates physical information with evolutionary techniques for improved solutions.

Findings

Neural networks reduce to Hypernetted Chain closure for hard sphere fluids.

Evolutionary optimization with physical constraints yields results comparable to molecular simulations.

Proposes new methods for solving the Ornstein-Zernike equation using computational intelligence.

Abstract

The main goal of this thesis is to provide an exploration of the use of computational intelligence techniques to study the numerical solution of the Ornstein-Zernike equation for simple liquids. In particular, a continuous model of the hard sphere fluid is studied. There are two main proposals in this contribution. First, the use of neural networks as a way to parametrize closure relation when solving the Ornstein-Zernike equation. It is explicitly shown that in the case of the hard sphere fluid, the neural network approach seems to reduce to the so-called Hypernetted Chain closure. For the second proposal, we explore the fact that if more physical information is incorporated into the theoretical formalism, a better estimate can be obtained with the use of evolutionary optimization techniques. When choosing the modified Verlet closure relation, and leaving a couple of free parameters to be adjusted, the results are as good as those obtained from molecular simulations. The thesis is then closed with a brief summary of the main findings and outlooks on different ways to improve the proposals presented here.