2019/02/07 by Chinmay S. Kulkarni, Kulkarni, Chinmay S.
Computer Science · Engineering · Physics and Astronomy · #Control Systems and Identification #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.1902.02719
openalex publication_date 2019/02/07 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
We study the performance of sparse regression methods and propose new\ntechniques to distill the governing equations of dynamical systems from data.\nWe first look at the generic methodology of learning interpretable equation\nforms from data, proposed by Brunton et al., followed by performance of LASSO\nfor this purpose. We then propose a new algorithm that uses the dual of LASSO\noptimization for higher accuracy and stability. In the second part, we propose\na novel algorithm that learns the candidate function library in a completely\ndata-driven manner to distill the governing equations of the dynamical system.\nThis is achieved via sequentially thresholded ridge regression (STRidge) over a\northogonal polynomial space. The performance of the three discussed methods is\nillustrated by looking the Lorenz 63 system and the quadratic Lorenz system.\n