Filtered Integral Formulation of the Sparse Model Identification Problem

This paper presents a generalized approach to identify the structure of governing nonlinear equations of motion from the time history of state variables and control functions. An integral form involving a low-pass filter in conjunction with sparse approximation tools is used to find a parsimonious model for underlying true dynamics from noisy measurement data. Two chaotic oscillatory systems as well as the well-known problem of identifying the central force field from position-only observation data are considered to validate the developed approach. The simulation results considered in the paper demonstrate the performance of the developed approach in learning unknown nonlinear system dynamics accurately with fewer basis functions as compared with classical least-squares regression techniques and emerging deep learning approaches. A comparison of the sparse identification techniques with classical least-squares regression techniques and emerging deep learning approaches reveals the utility of the methodology developed in the paper.