(195c) Learning Physically Informed Differential Viscoelastic Constitutive Models from Data

Constitutive models play a critical role in the engineering of products and processes involving viscoelastic materials. A substantial body of work has been dedicated to deriving these models for particular classes of materials directly from physical considerations. However, such models often cannot sufficiently describe the diverse response space of viscoelastic materials in various experimentally and industrially relevant flows, and many such models are too complex in form to enable forward predictions in complicated flows. Recently, the advent of widely available machine learning tools has given rise to a new approach: learning constitutive models directly from data. While these approaches have shown some success in very particular flows, they are in general not easily portable to different flow conditions, and tend to accommodate training data taken only by specific experimental protocols. Moreover, these approaches do not enforce key physical constraints such as invariance to rotating frames of reference, and the second law of thermodynamics. Here, we present a framework for learning physically informed differential constitutive models for viscoelastic fluids that combines many of the salient features of the previous approaches. These models, which we call “rheological universal differential equations” (rUDEs), are composed of the tensorial corotational Maxwell (CRM) model with an added tensor-valued neural network, which takes the rate-of-deformation and stress tensors as inputs. The CRM model provides an underlying viscoelastic structure to the model, and the neural network provides a tool for learning material-specific features. By constraining the structure of this neural network, we enforce that the learned model obeys the physical constraints of frame-invariance and thermodynamic stability. Moreover, because rUDEs are differential and tensorial in form, they may be trained on -- and ultimately used to predict -- any observable related to the stress or strain obtained in an arbitrary flow protocol. We demonstrate the predictive capabilities of rUDEs trained on both synthetic data from well-known constitutive models, as well as real data for a model viscoelastic system. These learned constitutive models are versatile and adaptable tools for making predictions about material properties in a variety of conditions, including via integration into computational fluid dynamics tools, which is made possible by the differential equation structure of rUDEs. With increased availability of a wide breadth of experimental data for specific materials, rUDEs open new avenues for efficient and accurate data-driven rheological modeling.