2017/09/05 by Hayden Schaeffer, Schaeffer, Hayden, Giang Tran +3 · 4 citations
Decision Sciences · Engineering · Physics and Astronomy · #15A12 #37N30 #65K10 #65L09 #65L99 #65P30 #Control Systems and Identification #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1709.01558
openalex publication_date 2017/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Learning governing equations from a family of data sets which share the same physical laws but differ in bifurcation parameters is challenging. This is due, in part, to the wide range of phenomena that could be represented in the data sets as well as the range of parameter values. On the other hand, it is common to assume only a small number of candidate functions contribute to the observed dynamics. Based on these observations, we propose a group-sparse penalized method for model selection and parameter estimation for such data. We also provide convergence guarantees for our proposed numerical scheme. Various numerical experiments including the 1D logistic equation, the 3D Lorenz sampled from different bifurcation regions, and a switching system provide numerical validation for our method and suggest potential applications to applied dynamical systems.