# An Introduction to Sparse Identification of Nonlinear Dynamics for Engineering Applications

arXiv: https://arxiv.org/abs/2607.15077 · HTML: https://mlsanity.com/paper/2607.15077/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 54 references that are in the map.
- First posted on arXiv 16 Jul 2026.

## Builds on (most cited first, 12 of 12)

- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
- [Sparse learning of stochastic dynamic equations](https://mlsanity.com/paper/1712.02432/) (2017)
- [Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders](https://mlsanity.com/paper/2201.05136/) (2022)
- [A unified sparse optimization framework to learn parsimonious physics-informed models from data](https://mlsanity.com/paper/1906.10612/) (2019)
- [SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning](https://mlsanity.com/paper/2403.09110/) (2024)
- [Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants](https://mlsanity.com/paper/2211.10575/) (2022)
- [Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data](https://mlsanity.com/paper/2402.15357/) (2024)
- [VENI, VINDy, VICI: a generative reduced-order modeling framework with uncertainty quantification](https://mlsanity.com/paper/2405.20905/) (2024)
- [Multi-Fidelity SINDy: Sparse Discovery of Nonlinear Dynamical Systems with Fidelity-Weighted Measurements](https://mlsanity.com/paper/2606.15690/) (2026)

## Abstract (arXiv)

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.