Dynamic system modelling is essential for tracking and, potentially, controlling a physical system. However, dynamic systems may evolve over time, potentially exhibiting previously unseen behaviours. The system model must adapt accordingly, ideally in real-time, by incorporating online measurements. This capability is crucial for developing predictive digital twins, with applications in predictive maintenance and control, and must remain effective even when bifurcation points in the system's dynamics are encountered. The proposed framework exploits the Extended Kalman Filter (EKF) for data assimilation and SINDy [1] to develop a flexible, physically consistent, data-driven model based on previously acquired data [2]. We demonstrate how this approach can identify emerging dynamics contributions initially not included in the system model, and conversely, how the filter can suitably improve the sparsity of this model. Special emphasis will be given to the analysis of Micro-ElectroMechanical Systems (MEMS) exhibiting complex dynamic behaviours. [1] S.L. Brunton, J.L. Proctor, J.N. Kutz. Discovering governing equations from data by sparse identification of nonlinear dynamical systems, Proceedings of the National Academy of Sciences 113 (15) 3932–3937, 2016. [2] L. Rosafalco, P. Conti, A. Manzoni, S. Mariani, A. Frangi. EKF-SINDy: Empowering the extended Kalman filter with sparse identification of nonlinear dynamics. Computer Methods in Applied Mechanics and Engineering 431, 117264, 2024.