Finding the Underlying Viscoelastic Constitutive Equation via Universal Differential Equations and Differentiable Physics
This work addresses the challenge of accurately modeling complex viscoelastic fluids for researchers in fluid mechanics and rheology, representing an incremental advancement by applying existing UDE methods to this specific domain.
The research tackled the problem of modeling viscoelastic fluids by using Universal Differential Equations and differentiable physics to reconstruct missing terms in constitutive models, testing on synthetic datasets for four models under various flow conditions, with results showing effective stress predictions for most models but limitations for the ePTT model.
This research employs Universal Differential Equations (UDEs) alongside differentiable physics to model viscoelastic fluids, merging conventional differential equations, neural networks and numerical methods to reconstruct missing terms in constitutive models. This study focuses on analyzing four viscoelastic models: Upper Convected Maxwell (UCM), Johnson-Segalman, Giesekus, and Exponential Phan-Thien-Tanner (ePTT), through the use of synthetic datasets. The methodology was tested across different experimental conditions, including oscillatory and startup flows. While the UDE framework effectively predicts shear and normal stresses for most models, it demonstrates some limitations when applied to the ePTT model. The findings underscore the potential of UDEs in fluid mechanics while identifying critical areas for methodological improvement. Also, a model distillation approach was employed to extract simplified models from complex ones, emphasizing the versatility and robustness of UDEs in rheological modeling.