Micro-actuators play a crucial role in achieving ultra-precision motion in the field of semiconductor equipment due to their exceptional response characteristics and micro-nano step size. However, nonlinear characteristics such as hysteresis and creep significantly limit the improvement of accuracy and stability. Traditional modeling methods suffer from issues like high computational cost, complex models, and inability to directly obtain inverse models. To overcome these challenges, this study introduces the sparse identification of nonlinear dynamics (SINDy) algorithm for optimizing parameter adaptation of model expressions and enhancing modeling accuracy. Firstly, an orthogonal candidate database of nonlinear elements is established using the SINDy algorithm. Then, sparse regression operators are combined with regularization to penalize the constructed model, resulting in a simplified framework expression that includes input and output variables. In order to address overfitting caused by decreased accuracy during sparse punishment in SINDy algorithm, this paper proposes an improved particle optimization algorithm with enhanced inertia weight inspired by cycloidal principle for parameter optimization on the framework expression of SINDy model. Experimental results demonstrate superior performance of the improved SINDy algorithm which not only reduces modeling costs and complexity but also significantly improves fitting accuracy compared to existing methods.