  Rheology plays a pivotal role in understanding the flow behavior of fluids by
discovering governing equations that relate deformation and stress, known as
constitutive equations. Despite the importance of these equations, current
methods for deriving them lack a systematic methodology, often relying on sense
of physics and incurring substantial costs. To overcome this problem, we
propose a novel method named Rheo-SINDy, which employs the sparse
identification of nonlinear dynamics (SINDy) algorithm for discovering
constitutive models from rheological data. Rheo-SINDy was applied to five
distinct scenarios, four with well-established constitutive equations and one
without predefined equations. Our results demonstrate that Rheo-SINDy
successfully identified accurate models for the known constitutive equations
and derived physically plausible approximate models for the scenario without
established equations. Notably, the identified approximate models can
accurately reproduce nonlinear shear rheological properties, especially at
steady state, including shear thinning. These findings validate the robustness
of Rheo-SINDy in handling data complexities and underscore its efficacy as a
tool for advancing the development of data-driven approaches in rheology.
