"SIMPLE": A data-driven framework for measuring and modeling polymers in complex flows

A grand challenge in materials processing is the rapid development of microscopic models for fluid structure and rheology in materials for which no first principles theory currently exists. Applying machine learning to fill this gap has been hindered by a lack of experiments to generate training data, and an absence of ML tools that enforce the known underlying mechanistic constraints of fluid mechanics. To address these challenges, we develop a "fluidic four-roll mill" that generates diverse complex flows that can be probed with scanning small-angle X-ray scattering (FFoRM-sSAXS) to simultaneously measure velocity and nanostructures fields. Based on these data-rich measurements, we develop an ML framework -- scattering-informed microstructure prediction during Lagrangian evolution (SIMPLE) -- in which FFoRM-sSAXS data are used to train a model to predict nanostructure evolution in arbitrary flows. We use deep learning approaches and neural differential equations to learn a reduced order model that incorporates known physics such as co-rotational invariance and material symmetries. The framework is tested on rigid rod polymers and compared to theory and bulk rheological data, demonstrating significant promise to enable rational, model-driven design of polymer flow processing.