The discovery of scientific laws from measurements is a significant intellectual milestone, and its motivation arises from the widespread occurrence of nonlinear dynamical systems in science and engineering. Understanding the governing equations, which often take the form of ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic differential equations (SDEs), is essential for accurate prediction, effective control, and informed decision-making [1, 2]. In many complex systems, the underlying dynamics remain poorly understood, which renders conventional modeling techniques based on first principles both challenging and, at times, intractable. To tackle the challenge of model discovery in dynamical systems, Sparse Identification of Nonlinear Dynamics (SINDy) [3] offers a data-driven solution. By the use of given measurements, SINDy constructs parsimonious models that capture the essential features of system dynamics without the need for detailed knowledge of the underlying physics. The strength of SINDy lies in its ability to identify sparse and interpretable models, based on the assumption that the system's dynamics can be represented as a sparse linear combination of candidate functions. This process involves iterative optimization through sparse regression [4] and the selection of the most relevant terms from a comprehensive library, which enables the discovery of governing equations that are both accurate and physically meaningful. Building on the idea of using sparse regression techniques to discover nonlinear dynamical systems, extensive research has been conducted to enhance the SINDy framework for various objectives or to apply it across diverse domains.