发表机构
Department of Aeronautics, Imperial College London; Department of Mechanical Engineering, University of Washington; NSF AI Institute in Dynamic Systems, University of Washington（伦敦帝国理工学院航空系; 华盛顿大学机械工程系; 华盛顿大学动态系统领域美国国家科学基金会人工智能研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
介绍工程应用中非线性动力学稀疏识别（SINDy）方法，通过对候选非线性项库稀疏回归解决代理建模局限性，教程介绍该方法及扩展，经案例研究表明其易实现且灵活，是工程应用有价值的识别工具。
AI 中文摘要
许多工程问题涉及控制方程表征不佳或仅部分已知的现象。神经网络等代理建模技术虽能捕捉系统行为，但需大量难以获取的训练数据集，且模型物理可解释性有限。稀疏识别非线性动力学（SINDy）方法通过对候选非线性项库进行稀疏回归，从小规模数据集中恢复可解释的控制方程，解决了上述两个局限性。本教程介绍了SINDy方法，并逐步介绍其主要扩展，从抗噪声弱形式和基于集成的变体到约束和可参数化公式。本文及配套教程分为三个部分：第一部分介绍标准SINDy算法并逐步扩展，让无先验知识读者能跟随步骤并将方法应用于自身问题；其余两部分给出详细案例研究，一是无人机系统识别，二是混沌热虹吸换热器。通过这些例子，旨在证明SINDy易于实现且足够灵活，可作为先进工程应用的有价值识别工具。
英文摘要
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.
Comments15 pages, 4 figures
