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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 under data sparse situations, such as when only 2 or 3 molecular masses are in the training set. However, neither approach to integrate theory provides advantages in accuracy or computational efficiency when greater coverage of the parameter space or quantities of experimental data are available, indicating that the greatest impact on predictability occurs in data sparse situations. More important than impacting the accuracy of predictions though, these hybrid models provide physical relationships, such as the molecular mass dependence of the critical point or the coefficients within a FH expression. They also afford determination of scaling behavior of theoretical parameters from cloud point experiments instead of more complicated methods. This aspect of physics-incorporated ML models enhances trust in predictions, as well as providing a systematic means to identify anomalous behavior, assess experimental data quality, and reveal unanticipated correlations among factors. |
