Adsorbate-adsorbent potential energy function from second virial coefficient data: a non-linear Hopfield Neural Network approach

The Hopfield Neural Network has been successfully applied to solve ill-posed inverse problems in different fields of chemistry and physics. In this work, the non-linear approach for this method will be applied to retrieve the empirical parameters of potential energy function, Ep(r)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_{p}(r)$$\end{document}, between adsorbate and adsorbent from experimental data. Since the adsorption data is related to the second virial coefficient and therefore to Ep(r)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_{p}(r)$$\end{document} through an integral equation, the Hopfield Neural Network will be used to find the best parameters which fits the experimental data. Initially simulated results will be analyzed to verify the method performance for data sets with and without noise addition. Then, experimental data for adsorption of propionitrile on activated carbon will be treated. Results presented here corroborate to the robustness of this method.