The formulation of rheological constitutive equations -- models that relate
internal stresses and deformations in complex fluids -- is a critical step in
the engineering of systems involving soft materials. While data-driven models
provide accessible alternatives to expensive first-principles models and less
accurate empirical models in many engineering disciplines, the development of
similar models for complex fluids has lagged. The diversity of techniques for
characterizing non-Newtonian fluid dynamics creates a challenge for classical
machine learning approaches, which require uniformly structured training data.
Consequently, early machine learning constitutive equations have not been
portable between different deformation protocols or mechanical observables.
Here, we present a data-driven framework that resolves such issues, allowing
rheologists to construct learnable models that incorporate essential physical
information, while remaining agnostic to details regarding particular
experimental protocols or flow kinematics. These scientific machine learning
models incorporate a universal approximator within a materially objective
tensorial constitutive framework. By construction, these models respect
physical constraints, such as frame-invariance and tensor symmetry, required by
continuum mechanics. We demonstrate that this framework facilitates the rapid
discovery of accurate constitutive equations from limited data, and that the
learned models may be used to describe more kinematically complex flows. This
inherent flexibility admits the application of these 'digital fluid twins' to a
range of material systems and engineering problems. We illustrate this
flexibility by deploying a trained model within a multidimensional
computational fluid dynamics simulation -- a task that is not achievable using
any previously developed data-driven rheological equation of state.Comment: 13 pages, 4 figure