Determination of thermodynamic state variables of liquids from their microscopic structures using an artificial neural network

Abstract

In this work we implement a machine learning method to predict the thermodynamic state of a liquid using only its microscopic structure provided by the radial distribution function (RDF). The main goal is to determine the equation of state of the system. The goal is achieved by predicting the density, temperature or both at the same time using only the RDF. We implement and train a machine learning feed forward artificial neural network (ANN) to address the different cases of interest where single or simultaneous predictions are done. Due to its versatility, in this study the Lennard-Jones (LJ) fluid is used as the reference system. The ANN is trained in a wide range of densities and temperatures, covering the liquid–vapour coexistence, liquid phase and supercritical states. We show that the overall percentage relative error of most of the predictions in different cases of study is around 3%. As a practical case of study we use the ANN predictions to determine the pressure equation of state for different isotherms and we found a very good agreement with respect to the exact results. Our ANN implementation is a versatile and useful tool to predict thermodynamic state variables when some information is unknown and, consequently, to enhance the thermodynamic description of liquids.