PySINDy: A Python package for the sparse identification of nonlinear dynamical systems from data

Authors of papers retaincopyright and release the workunder a Creative CommonsAttribution 4.0 InternationalLicense (CC-BY)Scientists have long quantified empirical observations by developing mathematical models that characterize the observations, have some measure of interpretability, and are capable of making predictions. Dynamical systems models in particular have been widely used to study, explain, and predict system behavior in a wide range of application areas, with examples ranging from Newton’s laws of classical mechanics to the Michaelis-Menten kinetics for modeling enzyme kinetics. While governing laws and equations were traditionally derived by hand, the current growth of available measurement data and resulting emphasis on data-driven modeling motivates algorithmic approaches for model discovery. A number of such approaches have been developed in recent years and have generated widespread interest, including Eureqa (Schmidt & Lipson, 2009), sure independence screening and sparsifying operator (Ouyang, Curtarolo, Ahmetcik, Scheffler, & Ghiringhelli, 2018), and the sparse identification of nonlinear dynamics (SINDy) (Brunton, Proctor, & Kutz, 2016). Maximizing the impact of these model discovery methods requires tools to make them widely accessible to scientists across domains and at various levels of mathematical expertise.This project is a fork of sparsereg( Quade, 2018). SLB acknowledges funding supportfrom the Air Force Office of Scientific Research (AFOSR FA9550-18-1-0200) and the ArmyResearch Office (ARO W911NF-19-1-0045). JNK acknowledges support from the Air ForceOffice of Scientific Research (AFOSR FA9550-17-1-0329). This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under GrantNumber DGE-1256082