A TUTORIAL FOR SPARSE IDENTIFICATION OF NONLINEAR DYNAMICAL SYSTEM (SINDy) FRAMEWORK TO DISCOVER GOVERNING EQUATIONS FROM RAW DATA

Abstract

The discovery of governing equation from time-series data is a challenge in the analysis of nonlinear dynamical systems. In this work, a clear and systematic exposition of the Sparse Identification of Nonlinear Dynamical System (SINDy) framework is presented for data-driven equation discovery. The method is formulated through system representation, construction of a candidate function library, and identification of sparse governing terms. The approach is validated using 1D, 2D, and 3D systems, including the logistic model, nonlinear pendulum, and Lorenz system. The coefficients we found shows that only the actual terms from the true equation are important, unnecessary terms are correctly ignored. These results show that SINDy is an effective method for discovering the governing equations of nonlinear physical systems directly from data.