A physics-enforced neural network to predict polymer melt viscosity

Achieving superior polymeric components through additive manufacturing (AM) relies on precise control of rheology. One rheological property particularly relevant to AM is melt viscosity (η). η is influenced by polymer chemistry, molecular weight (Mw), polydispersity, shear rate (γ̇\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\gamma}}$$\end{document}), and temperature (T). The relationship of η with Mw, γ̇\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\gamma }}$$\end{document}, and T is captured by parameterized equations. Several physical experiments are required to fit the parameters, so predicting η of new polymer materials in unexplored physical domains is laborious. Here, we develop a Physics-Enforced Neural Network (PENN) model that predicts the empirical parameters and encodes the parametrized equations to calculate η as a function of polymer chemistry, Mw, polydispersity, γ̇\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\gamma }}$$\end{document}, and T. We benchmark our PENN against physics-unaware Artificial Neural Network (ANN) and Gaussian Process Regression (GPR) models. We demonstrate that the PENN offers superior values of η when extrapolating to unseen values of Mw, γ̇\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\gamma }}$$\end{document}, and T for sparsely seen polymers.