Activity coefficients, which are a measure of the non-ideality of liquid mixtures, are a key property in chemical engineering with relevance to modeling chemical and phase equilibria as well as transport processes. Although experimental data on thousands of binary mixtures are available, prediction methods are needed to calculate the activity coefficients in many relevant mixtures that have not been explored to-date. In this report, we propose a probabilistic matrix factorization model for predicting the activity coefficients in arbitrary binary mixtures. Although no physical descriptors for the considered components were used, our method outperforms the state-of-the-art method that has been refined over three decades while requiring much less training effort. This opens perspectives to novel methods for predicting physico-chemical properties of binary mixtures with the potential to revolutionize modeling and simulation in chemical engineering. Activity Coefficients at Infinite Dilution   Solutes SolventsThis document is the unedited authors' version of a submitted work that was subsequently accepted for publication in TheIn this work, we describe a novel application of Machine Learning (ML) to the field of physical chemistry and thermodynamics: the prediction of physico-chemical properties of binary liquid mixtures by matrix completion. We focus on the prediction of a single property: the so-called activity coefficient, which is a measure of the non-ideality of a liquid mixture and of enormous relevance in practice. The interesting aspect of our approach is that no expert knowledge about the components that make up the mixture was used: all we needed was an incomplete, sparse data set of binary mixtures and their measured activity coefficients that our method was able to successfully complete. We show that this simple approach outperforms an established procedure that has been the state of the art for several decades.ML approaches to chemical and engineering sciences date back more than 50 years ago, but the genuine exploitation of the potential of ML in these fields has only recently begun 1 . An overview of recent advances in chemical and material sciences has, e.g., been given by Ramprasad et al. 2 and Butler et al. 3 ML has already been used to predict physico-chemical properties of mixtures, including activity coefficients 4-10 . Most of these approaches are basically quantitative structureproperty relationships (QSPR) methods 11 that use physical descriptors of the components as input data to characterize the considered mixtures and relate them to the property of interest by an ML algorithm, e.g., a neural network. However, the scope of these approaches is in general rather small.Binary mixtures are of fundamental importance in chemical engineering. The properties of mixtures can in general not be described based on properties of the pure components alone. If, however, the respective properties of the binary constituent 'sub-mixtures' of a multi-component mixture are known, the properties of the multi...

Activity coefficients describe the nonideality of liquid mixtures and are essential for calculating equilibria. The activity coefficients at infinite dilution in binary mixtures are particularly important as the activity coefficients at finite concentrations can be predicted based on their knowledge not only in binary mixtures but also in multicomponent mixtures. The available experimental data on these activity coefficients at infinite dilution in binary mixtures is readily accessible in databases and can be organized in a matrix with the rows representing the solutes and the columns representing the solvents or vice versa. As experimental data is lacking for many binary mixtures, this matrix is only sparsely populated. Filling its gaps using predictive methods is essential. Recently, matrix completion methods (MCMs) have been applied successfully for this purpose. However, only isothermal data sets have been considered. In the present work, we apply an MCM to predict activity coefficients at infinite dilution at varying temperatures. Furthermore, we show how one can incorporate physical knowledge on the nature of the temperature dependency of the activity coefficients at infinite dilution. The predictions obtained with this new approach outperform those obtained with the best currently available physical prediction method for activity coefficients at infinite dilution, the modified UNIFAC (Dortmund) method.

Activity coefficients describe the nonideality of liquid mixtures and are essential for calculating equilibria. The activity coefficients at infinite dilution in binary mixtures are particularly important as the activity coefficients at finite concentrations can be predicted based on their knowledge not only in binary mixtures but also in multicomponent mixtures. The available experimental data on these activity coefficients at infinite dilution in binary mixtures is readily accessible in databases and can be organized in a matrix with the rows representing the solutes and the columns representing the solvents or vice versa. As experimental data is lacking for many binary mixtures, this matrix is only sparsely populated. Filling its gaps using predictive methods is essential. Recently, matrix completion methods (MCMs) have been applied successfully for this purpose. However, only isothermal data sets have been considered. In the present work, we apply an MCM to predict activity coefficients at infinite dilution at varying temperatures. Furthermore, we show how one can incorporate physical knowledge on the nature of the temperature dependency of the activity coefficients at infinite dilution. The predictions obtained with this new approach outperform those obtained with the best currently available physical prediction method for activity coefficients at infinite dilution, the modified UNIFAC (Dortmund) method.

Knowledge of thermodynamic properties of mixtures is essential in many fields of science and engineering. However, the experimental data is usually scarce, so prediction methods are needed. Matrix completion methods have proven to be very successful in predicting thermodynamic properties of binary mixtures. In this approach, the experimental data is organized in a matrix whose rows and columns correspond to the two components, and whose entries indicate the value of the studied thermodynamic property at fixed conditions. In the present work, we extend the concept to tensor completion methods (TCMs). This allows to account for the variation of the studied property depending on the chosen conditions. The feasibility is demonstrated by applying a TCM to predict activity coefficients at infinite dilution. The third dimension of the tensor is used to describe the influence of the temperature. The TCM is shown to yield better predictions than the well‐established UNIFAC method. Furthermore, the proposed TCM is able to learn and unveil the physical law describing the temperature dependence of activity coefficients from the scarce experimental mixture data only.