Sparse identification of dynamic systems refers to the search for a reduced set of relevant variables that describe the behavior of complex systems based on data. This approach is fundamental in the analysis and modeling of systems and has been successfully applied in various fields of science and engineering. Computational models of cell electrophysiology are widely used to understand cardiac and neuro-pathologies and develop new therapies. However, some of these mathematical models involve hundreds of variables and complex biophysical details. In the context of cell electrophysiology, sparse identification of models will be explored to identify and simplify the Hodgkin-Huxley model, which is described by a set of ordinary differential equations. Initial experiments with synthetic data from the classical Hodgkin-Huxley model show promising results using the SINDy method to obtain a simplified, reduced, and polynomial version of the Hodgkin-Huxley dynamics.