(422a) Simple (Scattering-Informed Microstructure Prediction during Lagrangian Evolution) – a Data-Driven Framework for Modeling Complex Fluids

An overarching challenge in rheological practice is the rapid development of microscopic predictive models of fluid structure and rheology in material classes for which no first principles physics-based models currently exist. Progress in machine learning algorithms has facilitated dramatic improvements in data-driven modeling in many scientific fields, but purely data-driven rheological models have largely lagged behind. This is primarily due to a lack of experimental methods for generating training data sets, as well as an absence of machine learning approaches to efficiently train models that enforce the underlying mechanistic constraints of the material.

We address these challenges using the recently developed fluidic four-roll mill with scanning small-angle X-ray scattering (FFoRM-sSAXS), which can rapidly generate a large data set of nanostructural measurements along diverse 2D Lagrangian deformation trajectories. We propose a machine learning framework in which FFoRM-sSAXS data is used to train a model which can predict the nanostructural evolution of the fluid for an arbitrary deformation (velocity gradient tensor) input. We use deep learning approaches including autoencoders and neural ordinary differential equations to learn a computationally efficient reduced order model. We also learn a transformation from the state data embedded in the scattering intensity to the stress exerted on the fluid. We incorporate frame indifference and material symmetries by performing data-driven operations in a co-rotating, phase-aligned frame determined completely by the deformation input. The framework is tested on a rigid rod suspension and compared to theoretical constitutive models and bulk rheological data.