Title: Rheo-SINDy: Finding a Constitutive Model from Rheological Data for Complex Fluids Using Sparse Identification for Nonlinear Dynamics

Abstract: Rheology plays a pivotal role in understanding and predicting material behavior by discovering governing equations that relate deformation and stress, known as constitutive equations. Despite the critical importance of constitutive equations in predicting dynamics of complex fluids, a systematic methodology for deriving these equations from available data has remained a significant challenge in the field. To overcome the problem, we propose a novel method named Rheo-SINDy, which employs the sparse identification of nonlinear dynamics (SINDy) for discovering constitutive models from rheological data. Rheo-SINDy was applied to five distinct scenarios, including four cases with well-established constitutive equations and one without predefined equations. Our results demonstrate that Rheo-SINDy successfully identifies accurate models for the known constitutive equations and derives physically plausible approximate models for the scenario with the unknown one. These findings validate the robustness of Rheo-SINDy in handling real-world data complexities and underscore its efficacy as a powerful tool for advancing the development of data-driven approaches in rheology.