Many of the existing offline system identification methods cannot completely comprehend the dynamics of an evolving complex process without relying on impractically large data sets. As a solution to this, a systematic procedure capable of identifying and predicting the nonlinear dynamics on the fly promises to provide a useful representation of the process model. Motivated by this, an adaptive model identification framework that relies on the methods of sparse regression and feature selection is presented in this work. The proposed method is a three-step procedure: (1) identifying potential functions from a candidate library using recently developed Sparse Identification of Nonlinear Dynamics (SINDy), (2) updating coefficients of the identified model using ordinary least-squares regression, (3) selecting the most important features using stepwise regression. The proposed algorithm is implemented as follows. Initially, a baseline model is identified offline using SINDy, and as a new data becomes available, the subsequent online steps are triggered based on a pre-specified tolerance to further update the model. Such an adaptive identification scheme facilitates in perceiving the model structure using a less amount of data than its offline counterpart, SINDy. To highlight its significance, the dynamics of a continuous stirred tank reactor is identified using the proposed adaptive method and is compared with a model identified using SINDy alone. Published by Elsevier B.V. on behalf of Institution of Chemical Engineers.