Machine Learning in Thermodynamics: Prediction of Activity Coefficients by Matrix Completion

Abstract

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...

Hybridizing physical and data-driven prediction methods for physicochemical properties

“…In previous work 15 , we have introduced a novel, purely datadriven approach to predict physicochemical properties of mixtures. Specifically, we considered activity coefficients at infinite dilution γ ∞ i j in binary mixtures at a constant temperature, but this approach generalizes to other properties.…”

“…for not yet studied mixtures, can be framed as a matrix completion problem. [17][18][19][20] The basis of our previously introduced approach 15 is a probabilistic matrix completion method (MCM). We modeled ln γ ∞ i j (the logarithm of γ ∞ i j is used for scaling purposes) as a stochastic function of initially unknown features of the solutes i and solvents j, specifically as the dot product of two vectors:…”

Neural recommender system for the activity coefficient prediction andUNIFACmodel extension of ionicliquid‐solutesystems

“…The common idea is that the underlying associations or interactions are studied as links between entities represented using nodes in a network and the problem is reduced to predict future or tentative associations/interactions among these nodes. Hence, the recommender techniques or algorithms can be extended to similar problems, including the completion of γ ∞ database focused here 37 . Furthermore, deep learning has recently been revolutionizing the recommendation architectures dramatically, which bring more opportunities to improve the recommender performance by overcoming obstacles of conventional RS models 38 .…”

“…Hence, the recommender techniques or algorithms can be extended to similar problems, including the completion of γ ∞ database focused here. 37 Furthermore, deep learning has recently been revolutionizing the recommendation architectures dramatically, which bring more opportunities to improve the recommender performance by overcoming obstacles of conventional RS models. 38 DNN-based RS enables the codification of more complex abstractions as data representations in the higher layers and the effective capture of non-linear links between entities, which particularly fits the requirements for solute-in-IL γ ∞ matrix completion task.…”

Using a machine learning model for the optimal design of simulated moving bed processes and its application to separate rebaudioside A and stevioside

“…In particular, deep learning has become a popular machine learning technique due to its successful applications in speech recognition, image recognition, and natural language processing 4 . In the field of chemical engineering, the application of machine learning has also been developed rapidly 5 for purposes such as process monitoring and online optimization, 6,7 fault detection and diagnosis, 8,9 as well as the construction of prediction models 10‐13 …”