2024/12/31 by Elias C. Rodrigues, Roney L. Thompson, Rodrigues, Elias C. +5 · 1 citation
Chemical Engineering · Engineering · #Dynamics and Control of Mechanical Systems #FOS: Computer and information sciences #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Machine Learning (cs.LG) #Rheology and Fluid Dynamics Studies #Vibration and Dynamic Analysis
paper · pdf · doi:10.48550/arxiv.2501.00556
openalex publication_date 2024/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.