Fitting three dimensional constitutive models to low dimensional data using differentiable rheometry

Accurately representing the constitutive law of a viscoelastic fluid is crucial to successfully simulate the fluid’s response in novel geometries and under untested loading conditions. However, fitting a full tensorial constitutive law to typical experimental data is difficult with traditional techniques, due in large part to the fact that many experiments can only measure one or two dimensions of the six coupled stress components.

In recent years, neural network-based approaches have been suggested to enable one to learn mathematically consistent rheological laws from data. However, such approaches struggle to generalize to arbitrary forcings and geometries and lack physical interpretability within existing rheological frameworks. We instead present an alternative approach that applies machine learning tools to fit known constitutive models onto limited experimental data, improving physical interpretability while offering estimates for the accuracy of such approaches. With this approach, we are able to also explore problems with model identifiability under typical experimental methodologies and propose alternative experimental techniques to improve data fitting.