A Physics-Informed Machine Learning Model for Polymer Melt Viscosity

Polymer-melt processing is highly dependent on the rheological properties of a given polymer, including melt viscosity. For novel polymers and processes to be industrially viable, the in-situ viscosity must be appropriate for the given application. This viscosity is dependent not only on the polymer identity, but also on the molecular weight (or polydispersity), induced shear rate, and processing temperature. Though phenomenological relationships, motivated by known underlying physics are commonly used to relate these environmental factors to the viscosity, such relationships involve empirical constants obtained by fitting measurements to the phenomenological equations. Predictions of viscosity for new cases are thus generally difficult due to the unavailability of the empirical parameters. Here, we adopt a data-driven approach, with or without physical equation augmentation to predict a set of machine learned models to predict the melt viscosity of polymers as a function of molecular weight, shear rate, and temperature. Our ML models were trained on a data set of 1903 melt-viscosity values pertaining to 93 distinct polymers. Two models, one based on Gaussian-Process Regression (GPR) and the second on Artificial Neural Network (ANN) were first employed, devoid of any physical equation, and trained on the melt-viscosity dataset. Next, we created a HyperNetwork architecture that encodes the known viscosity equations. All three models are critically evaluated to determine the limits of the models with no encoded physics and the extrapolative capabilities of the physics-informed model.