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 ( \({\dot{\gamma}}\) ), and temperature (T). The relationship of η with Mw, \({\dot{\gamma }}\) , 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, \({\dot{\gamma }}\) , 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, \({\dot{\gamma }}\) , and T for sparsely seen polymers.