Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology

Abstract

Recent advances in data-driven modelling have highlighted the potential of hybrid approaches which combine Tensor Basis Neural Networks (TBNN) with Universal Differential Equations (UDE) to discover frame-invariant, non-linear viscoelastic constitutive models. These hybrid models enable the creation of digital twins for complex viscoelastic fluids, offering direct transferability to computational fluid dynamics simulations. In this work, we introduce a reduced dimensional tensor basis formulation that enhances both the physical consistency of the learned representations with respect to the training data and the numerical stability of subsequent simulations. The UDE architecture is embedded into an open-source finite volume solver in which the constitutive response is generated dynamically at runtime based on local fluid flow conditions. Training on synthetic datasets generated using a range of well established viscoelastic models in oscillatory shear flows alone, the performance of the resulting UDEs is evaluated under extrapolation to unseen conditions and flow-types. These include deploying the UDEs in viscometric extensional flows as well as 2D and 3D benchmark flows, such as the 4:1 sudden contraction and cross-slot, providing a quantitative analysis of their capabilities, limitations and failure modes. The proposed reduced-basis framework enables data-efficient discovery of frame-invariant constitutive models that generalise beyond their training regime, capturing key flow features such as the onset and growth of flow-induced elastic instabilities in strong extensional flows even though trained solely on shear data. Quantitative accuracy decreases as extrapolation increases, but incorporating first normal stress difference information further improves quantitative accuracy and extends predictive fidelity to higher Deborah numbers.