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Integrating theory with machine learning for predicting polymer solution phase behavior



Jeffrey Ethier, Debra Audus, Devin Ryan, Richard Vaia


Flory-Huggins (FH) theory is foundational to understanding macro-phase separation in polymer solutions; however, its predictions often quantitatively disagree with experiment. Recent machine-learning (ML) methods have generated predictive models of phase behavior across a broad range of chemistries and state variables with uncertainty comparable to experiment, but they lack interpretability. In this work, we develop several hybrid frameworks that combine Flory-Huggins theory with ML to (i) further improve interpolation and extrapolation with less experimental data, as well as (ii) provide interpretability of the ML model. Using the well-studied binodal of polystyrene-cyclohexane as a case study, we compare data-derived ML models to hybrid models where the prediction is confined by a theoretical expression (theory-constrained model), or the feature vector input incorporates theoretical expressions (theory-informed model). Even though Flory-Huggins theory is imperfect, its incorporation improves performance when only 2 or 3 molecular masses are in the training set. However, the theory-constrained formulation requires significantly more data than the theory-informed models. Neither however provides advantages in accuracy or computational efficiency when greater coverage of the parameter space or quantities of experimental data are available, likely due to limitations of the theory. Even so, these hybrid models provide physical relationships, such as the molecular mass dependence of the critical point or of the coefficients within a FH expression. This aspect of physics-incorporated ML models not only enhances trust in predictions, but also provides a systematic means to identify anomalous behavior, and subsequently assess experimental data quality or reveal unanticipated correlations among factors.


Ethier, J. , Audus, D. , Ryan, D. and Vaia, R. (2023), Integrating theory with machine learning for predicting polymer solution phase behavior, Giant, [online],, (Accessed April 18, 2024)
Created May 31, 2023, Updated June 2, 2023