Efficient estimation of second virial coefficients of fused hard-sphere molecules by an artificial neural network

Abstract

A method for estimation of second virial coefficients of non-flexible, hard molecules in a neat fluid by artificial neural networks (ANN) is described. The ANN technique is able to predict the second virial coefficients with far less computational effort than the usual method, based on integral evaluation, particularly for large molecules. The neural network is composed of three layers (with two active layers); the input layer contains 21 neurons, the second layer contains four neurons and the third (output) layer just one neuron, whose output is an estimate of the second virial coefficient. The ANN was trained by the back-propagation method, taking fused hard-spheres, ellipsoids of revolution and prolate spherocylinders as the training set. The inputs to the ANN are the so-called volumetric autocorrelation array plus two additional shape descriptors of easy calculation. The volumetric autocorrelation is the distribution of distances between two points within the molecule. This work is a first step in the development of an equation of state for hard fluid mixtures, whose parameters are determined by neural networks.