Finding the Underlying Viscoelastic Constitutive Equation via Universal Differential Equations and Differentiable Physics

TL;DR

This paper introduces a novel approach combining Universal Differential Equations and differentiable physics to identify viscoelastic constitutive equations, demonstrating effectiveness across multiple models and experimental conditions with some limitations.

Contribution

It presents a new methodology using UDEs and neural networks to reconstruct viscoelastic constitutive models from synthetic data, including a model distillation technique.

Findings

UDEs accurately predict stresses in most viscoelastic models

The approach works well across different flow conditions

Some limitations observed with the ePTT model

Abstract

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.