An Introduction to Sparse Identification of Nonlinear Dynamics for Engineering Applications

2026-07-16

AI Summary

This work addresses the challenge of identifying governing equations in engineering systems where physical models are unknown or incomplete, and conventional data-driven approaches often require extensive datasets while lacking interpretability. Building upon the Sparse Identification of Nonlinear Dynamics (SINDy) framework, the study develops enhanced variants—incorporating noise robustness, weak-form formulations, ensemble learning, and parameterization—to recover interpretable dynamical equations from limited observational data via sparse regression. The project bridges the gap between SINDy theory and practical engineering deployment by establishing a flexible, user-friendly system identification framework, accompanied by open-source tutorials and case studies. The methodology is successfully validated on real-world applications, including unmanned aerial vehicle system identification and modeling of a chaotic thermosyphon heat exchanger, demonstrating its effectiveness and practical utility in authentic engineering scenarios.

Abstract

Many engineering problems involve phenomena whose governing equations are poorly characterized or only partially known. Surrogate modeling techniques such as neural networks can capture the behavior of these systems, but they typically demand large training datasets that are difficult to obtain in engineering contexts and yield models with limited physical interpretability. The Sparse Identification of Nonlinear Dynamics (SINDy) method addresses both limitations by performing sparse regression over libraries of candidate nonlinear terms, recovering interpretable governing equations from comparatively small datasets. Although SINDy has been demonstrated extensively on canonical benchmark systems, its application to practical engineering problems is less widely documented. This tutorial introduces the SINDy method and progressively builds toward its main extensions, from noise-robust weak-form and ensembling-based variants to constrained and parametrizable formulations. The paper and the accompanying tutorial (available at https://github.com/paullililili/SINDy4Engineers) is organized in three parts: the first introduces the standard SINDy algorithm and progressively extends it, inviting readers without prior knowledge to follow each step and adapt the methods to their own problems; the remaining two parts present detailed case studies on (1) the system identification of an unmanned aerial vehicle and (2) a chaotic thermosyphon heat exchanger. Through these examples, we aim to demonstrate that SINDy is simple to implement yet flexible enough to serve as a valuable identification tool for advanced engineering applications.

Problem

• governing equations
• surrogate modeling
• physical interpretability
• system identification
• engineering applications

Innovation

• SINDy
• sparse regression
• system identification
• interpretable modeling
• nonlinear dynamics