An artificial neural network model for the unary description of pure substances and its application on the thermodynamic modelling of pure iron

Abstract

AbstractThe aim of this work is to introduce a novel approach for the universal description of the thermodynamic functions of pure substances on the basis of artificial neural networks. The proposed approximation method is able to describe the thermodynamic functions ($$C_{p}(T), S(T), H(T)-H(T_{\mathrm{ref}}), G(T)$$ C p ( T ) , S ( T ) , H ( T ) - H ( T ref ) , G ( T ) ) of the different phases of unary material systems in a wide temperature range (between 0 and 6000 K). Phase transition temperatures and the respective enthalpies of transformation, which are computationally determined by the minimization of the Gibbs free energy, are also approximated. This is achieved by using artificial neural networks as models for the thermodynamic functions of the individual phases and by expressing the thermodynamic quantities in terms of the free network parameters. The resulting expressions are then optimized with machine learning algorithms on the basis of measurement data. A physical basis for the resulting approximation is given by the use of, among others, Planck–Einstein functions as activation function of the neurons of the network. This article provides a description of the method and as an example of a specific application the approximation of the thermodynamic functions of the different phases of pure iron. The article focuses on the problem of the representation of thermodynamic data and their practical application.