Modeling the non-linear dynamics of a system from measurement data accurately is an open challenge. Over the past few years, various tools such as SINDy and DySMHO have emerged as approaches to distill dynamics from data. However, challenges persist in accurately capturing dynamics of a system especially when the physical knowledge about the system is unknown. A promising solution is to use a hybrid paradigm, that combines mechanistic and black-box models to leverage their respective strengths. In this study, we combine a hybrid modeling paradigm with sparse regression, to develop and identify models simultaneously. Two methods are explored, considering varying complexities, data quality, and availability and by comparing different case studies. In the first approach, we integrate SINDy-discovered models with neural ODE structures, to model unknown physics. In the second approach, we employ Multifidelity Surrogate Models (MFSMs) to construct composite models comprised of SINDy-discovered models and error-correction models.