Prediction of the density of aqueous electrolyte solutions with matrix completion methods

Abstract

Information on the density of electrolyte solutions is important for many processes in chemistry and chemical engineering. However, experimental data are scarce, and broadly applicable prediction methods that can extrapolate to unstudied electrolytes have been unavailable until now. In the present work, we introduce a novel approach for predicting the densities of aqueous solutions of 720 single electrolytes at 298.15 K based on the machine-learning concept of matrix completion. The studied electrolytes belong to the valency classes 1:1, 2:1, 1:2, 3:1, 2:2, and 3:2; individual ion concentrations up to 0.1 mol/mol are considered. We arrange the available density data for these electrolytes composed of 40 cations and 18 anions in a matrix, where the columns and rows denote the cations and anions, respectively. In the literature, experimental data are available for only 181 of all 720 electrolytes. This makes the prediction for the other electrolytes a matrix completion problem, which we address using probabilistic matrix factorization. To account for the concentration dependence of the density, a dimensionality reduction is carried out by representing the density as a linear function of the mole fraction-based ionic strength, a correlation found to be very accurate for all considered electrolytes. As a result, a sparse matrix containing the scalar slope of that linear function is obtained. Two matrix completion methods (MCMs) are introduced: a purely data-driven one trained only on the available density data and a hierarchical model that includes the ions’ valencies as side information. The performance of both models is evaluated on unseen test data, with the hierarchical MCM providing very accurate predictions: When averaging the relative deviations for all density data points for a certain electrolyte, an average deviation of 0.96 % is obtained. Moreover, we show that the MCM parameters learned during training are physically interpretable, as their values align with descriptors such as an ion’s charge density.