PySINDy: A comprehensive Python package for robust sparse system identification

TL;DR

PySINDy is a Python package that advances data-driven modeling by enabling robust discovery of complex differential equations from noisy, limited data using new algorithms, extended candidate libraries, and stability techniques.

Contribution

The paper introduces major updates to PySINDy, including advanced features for identifying general differential equations, new optimization algorithms, and capabilities like constrained PDE discovery and ensembling.

Findings

Enhanced ability to identify actuated systems and PDEs from noisy data

Implementation of robust formulations like integral SINDy and ensembling techniques

Introduction of new sparse regression algorithms for model stability and constraints

Abstract

Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools for applying the sparse identification of nonlinear dynamics (SINDy) approach to data-driven model discovery. In this major update to PySINDy, we implement several advanced features that enable the discovery of more general differential equations from noisy and limited data. The library of candidate terms is extended for the identification of actuated systems, partial differential equations (PDEs), and implicit differential equations. Robust formulations, including the integral form of SINDy and ensembling techniques, are also implemented to improve performance for real-world data. Finally, we provide a range of new optimization algorithms, including several sparse regression techniques and algorithms to enforce and promote inequality constraints and stability. Together, these updates enable entirely new SINDy model discovery capabilities that have not been reported in the literature, such as constrained PDE identification and ensembling with different sparse regression optimizers.