Systematic model reduction for constitutive equations: Improving the accuracy of tractable models of entangled polymer rheology

Accurate and efficient constitutive modelling of entangled polymer melts remains a central challenge in non-Newtonian fluid mechanics. While the GLaMM model captures accurately many nonlinear flow experiments, its computational cost renders it impractical for many applications, particularly those requiring numerous evaluations of the model such as polydispersity or complex flow. In contrast, the Rolie-Poly model, a simplified reduction of GLaMM, is widely used in industrial and computational contexts due to its speed, despite limitations in predictive accuracy. This work introduces a novel physics-constrained, data-driven model reduction framework for externally driven partial differential equations (PDEs), applied here to the GLaMM model. The approach leverages a set of manually selected, slow-evolving coarse-grained variables to characterise the full model configuration. Rather than deriving explicit evolution equations for these variables, we interpolate from precomputed GLaMM data to reconstruct the full configuration and compute time derivatives using the original PDE. Solving for the reduced variables permits significantly larger timesteps while retaining the accuracy of the full model. Unlike most data-driven methods that learn purely from data, our approach employs a lift–evaluate–project cycle, leveraging the original nonlinear, fine-grained physics at each step to ensure physical consistency. We demonstrate the framework’s effectiveness by constructing a reduced model that achieves the accuracy of the GLaMM model with timestep requirement comparable to Rolie-Poly. Working with a single chain length Z = 25 as an exemplar, the reduced model is validated for both uniaxial extension and shear flows, including time-dependent cases, and shows strong agreement with GLaMM model predictions across a range of Weissenberg numbers. However, further key work is required to produce, from our approach, a full constitutive equation capable of replacing the Rolie-Poly model in Computational Fluid Dynamics simulations. We have identified and discussed these key steps. This work opens several avenues for future applications to polydisperse systems, flow-induced crystallisation, and other multiscale rheological phenomena. • A framework to reduce full-chain molecular models to tractable constitutive equations. • Exploits both synthetic data and the underlying full-chain physics. • Produces a reduced model with the GLaMM model’s accuracy and the Rolie-Poly’s tractability.