Paper Number
SC19   James Swan Memorial Symposium 

Session
Suspensions and Colloids

Title
Learning physically-informed differential viscoelastic constitutive equations from data

Presentation Date and Time
October 10, 2022 (Monday) 6:05

Track / Room
Track 1 / Sheraton 4

Authors (Click on name to view author profile)

1. Lennon, Kyle R. (Massachusetts Institute of Technology, Chemical Engineering)
2. McKinley, Gareth H. (Massachusetts Institute of Technology, Mechanical Engineering)
3. Swan, James W. (Massachusetts Institute of Technology, Chemical Engineering)

Author and Affiliation Lines (in printed abstract book)
Kyle R. Lennon¹, Gareth H. McKinley² and James W. Swan^1
1Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139; ²Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02142

Speaker / Presenter 
Lennon, Kyle R.

Keywords
theoretical methods; computational methods; AI based; ML based

Text of Abstract
Although a substantial body of work has been dedicated to deriving viscoelastic constitutive equations for particular classes of materials directly from physical considerations, these models often cannot sufficiently describe the diverse response space of viscoelastic materials in common experimentally and industrially relevant conditions. Recently, the advent of widely available machine learning (ML) tools has given rise to a new approach: learning constitutive models directly from data. While current ML approaches have shown some success in very particular circumstances, they are not easily portable to different flow conditions, tend to accommodate training data taken only by specific experimental protocols, and do not enforce key physical constraints such as invariance to rotating frames of reference. Here, we present a framework for learning physically-informed differential viscoelastic constitutive equations that combines the salient features of ML and physically-informed approaches. These models, which we call “rheological universal differential equations” (RUDEs), comprise the upper-convected Maxwell (UCM) model as a foundation with an added tensor-valued neural network, which takes the rate-of-deformation and deviatoric stress tensors as inputs. The UCM model provides a viscoelastic scaffolding for the model, allowing the neural network to rapidly learn material-specific features while preserving constraints such as frame invariance. 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 measured in an arbitrary flow protocol. We demonstrate these capabilities using RUDEs trained on both synthetic data from well-known constitutive models, and experimental data describing prototypical viscoelastic materials. With the increased availability of a wide breadth of experimental data for viscoelastic materials, RUDEs open new avenues for efficient and accurate data-driven rheological modeling.