Open-Source Dynamical Systems Research, with a Side of (Francis) Bacon

Abstract

Sparse Identification of Nonlinear dynamics (SINDy) is a family of methods for explicitly identifying differential equations from data. The open-source Python package pysindyprovides the engineering to support ongoing SINDy research. I discuss original and community innovations in smoothing and sparse optimization, as well as a colocation approach to simultaneous estimation of states and sparse coefficients. The compatibility of these methods through the pysindy API has lessons for mathematics as an experimental field. My contribution to the state of the art includes both original innovations and ongoing support for research contributions from the community. These innovations include smoothing methods such as kernel and Kalman, and sparse regression approaches involving Monte Carlo estimation, physics constraints, or mixed-integer optimization. The pysindy changes have also allowed a principled approach to simultaneous optimization of states and coefficients. Across these projects and more, the requirement for a consistent API has given rise to a common experimental language. This defense codifies that language in additional pacakges and suggests useful lessons for the open-source, numerical lab.