  In order to extract governing equations from time-series data, various
approaches are proposed. Among those, sparse identification of nonlinear
dynamics (SINDy) stands out as a successful method capable of modeling
governing equations with a minimal number of terms, utilizing the principles of
compressive sensing. This feature, which relies on a small number of terms, is
crucial for interpretability. The effectiveness of SINDy hinges on the choice
of candidate functions within its dictionary to extract governing equations of
dynamical systems. A larger dictionary allows for more terms, enhancing the
quality of approximations. However, the computational complexity scales with
dictionary size, rendering SINDy less suitable for high-dimensional datasets,
even though it has been successfully applied to low-dimensional datasets. To
address this challenge, we introduce iterative SINDy in this paper, where the
dictionary undergoes expansion and compression through iterations. We also
conduct an analysis of the convergence properties of iterative SINDy.
Simulation results validate that iterative SINDy can achieve nearly identical
performance to SINDy, while significantly reducing computational complexity.
Notably, iterative SINDy demonstrates effectiveness with high-dimensional
time-series data without incurring the prohibitively high computational cost
associated with SINDy.
