Constitutive laws characterise the stress-strain relationship in a material. Determining a consti-
tutive law experimentally typically involves subjecting the material to a prescribed deformation
and measuring the force required to achieve it. There are numerous constitutive laws which
have been developed to model the stress response of viscoelastic fluids, and the decision on
which constitutive law should be fitted to data is largely based on the rheologist’s knowledge
about the fluid in relation to the catalogue of standard models appearing in the literature. In
this thesis, we present an alternative approach for determining a viscoelastic fluid’s constitutive
law based on methods related to Koopman operator theory and Dynamic Mode Decomposition
in the context of control. Our approach systematically extracts the material parameters that
arise in stress-evolution equations of viscoelastic fluids directly from simulation or experimen-
tal data. We will present results from various applications of the framework that highlight
its accuracy and robustness in identifying material parameters and reconstructing the under-
lying constitutive law. We will discuss how data should be supplied to the method, and also
demonstrate how data from recently developed experimental protocols, as well as combined
data from multiple experiments, can be used to improve resolution. Finally, we will show that
our approach provides a natural way to utilise data from the nonlinear regime and extends to
higher-dimensional data sets where spatial data within a sample is available.Open Acces
