Using Computational Intelligence for solving the Ornstein-Zernike equation (2201.05089v2)

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.