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The discovery of governing differential equations from data is an open frontier in machine learning. The sparse identification of nonlinear dynamics (SINDy) \citep{brunton_discovering_2016} framework enables data-driven discovery of…

Machine Learning · Computer Science 2023-10-10 Mozes Jacobs , Bingni W. Brunton , Steven L. Brunton , J. Nathan Kutz , Ryan V. Raut

Identifying dynamical systems characterized by nonlinear parameters presents significant challenges in deriving mathematical models that enhance understanding of physics. Traditional methods, such as Sparse Identification of Nonlinear…

Machine Learning · Computer Science 2025-08-12 Siva Viknesh , Younes Tatari , Chase Christenson , Amirhossein Arzani

The sparse identification of nonlinear dynamical systems (SINDy) is a data-driven technique employed for uncovering and representing the fundamental dynamics of intricate systems based on observational data. However, a primary obstacle in…

Dynamical Systems · Mathematics 2025-09-23 Ali Forootani , Harshit Kapadia , Sridhar Chellappa , Pawan Goyal , Peter Benner

This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…

Optimization and Control · Mathematics 2015-04-27 Wei Pan , Ye Yuan , Jorge Gonçalves , Guy-Bart Stan

The Sparse Identification of Nonlinear Dynamics (SINDy) framework has been frequently used to discover parsimonious differential equations governing natural and physical systems. This includes recent extensions to SINDy that enable the…

Numerical Analysis · Mathematics 2026-01-21 Mohammed Alanazi , Majid Bani-Yaghoub

Sparse regression has emerged as a popular technique for learning dynamical systems from temporal data, beginning with the SINDy (Sparse Identification of Nonlinear Dynamics) framework proposed by arXiv:1509.03580. Quantifying the…

Methodology · Statistics 2023-08-21 Sara Venkatraman , Sumanta Basu , Martin T. Wells

A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary…

Machine Learning · Computer Science 2024-10-04 Doris Voina , Steven Brunton , J. Nathan Kutz

Modern societies have an abundance of data yet good system models are rare. Unfortunately, many of the current system identification and machine learning techniques fail to generalize outside of the training set, producing models that…

Systems and Control · Electrical Eng. & Systems 2023-11-27 Gabriel F. Machado , Morgan Jones

Sparse Identification of Nonlinear Dynamical Systems (SINDy) is a powerful tool for the data-driven discovery of governing equations. However, it encounters challenges when modeling complex dynamical systems involving high-order derivatives…

Dynamical Systems · Mathematics 2024-11-05 Haoyang Zheng , Guang Lin

Big data has become a critically enabling component of emerging mathematical methods aimed at the automated discovery of dynamical systems, where first principles modeling may be intractable. However, in many engineering systems, abrupt…

Data Analysis, Statistics and Probability · Physics 2018-08-01 Markus Quade , Markus Abel , J. Nathan Kutz , Steven L. Brunton

We consider the data-driven discovery of governing equations from time-series data in the limit of high noise. The algorithms developed describe an extensive toolkit of methods for circumventing the deleterious effects of noise in the…

Machine Learning · Computer Science 2022-01-03 Charles B. Delahunt , J. Nathan Kutz

The sparse identification of nonlinear dynamics (SINDy) has been established as an effective technique to produce interpretable models of dynamical systems from time-resolved state data via sparse regression. However, to model parameterized…

Dynamical Systems · Mathematics 2024-05-15 Javier A. Lemus , Benjamin Herrmann

Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using…

Dynamical Systems · Mathematics 2016-05-24 Steven L. Brunton , Joshua L. Proctor , J. Nathan Kutz

The combination of machine learning (ML) and sparsity-promoting techniques is enabling direct extraction of governing equations from data, revolutionizing computational modeling in diverse fields of science and engineering. The discovered…

Systems and Control · Electrical Eng. & Systems 2026-05-12 Mohammad Amin Basiri , Sina Khanmohammadi

This paper proposes a sparse identification of nonlinear dynamics (SINDy) with control and exogenous inputs for highly accurate and reliable prediction. Although SINDy is recognized as a remarkable approach for identifying nonlinear…

Systems and Control · Electrical Eng. & Systems 2025-10-21 Shuichi Yahagi , Ansei Yonezawa , Hiroki Seto , Heisei Yonezawa , Itsuro Kajiwara

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…

The Sparse Identification of Nonlinear Dynamics (SINDy) is a method for discovering nonlinear dynamical system models from data. Quantifying uncertainty in SINDy models is essential for assessing their reliability, particularly in…

Machine Learning · Computer Science 2025-07-17 Urban Fasel

Hybrid systems are traditionally difficult to identify and analyze using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations…

Dynamical Systems · Mathematics 2019-06-19 Niall M Mangan , Travis Askham , Steven L Brunton , J Nathan Kutz , Joshua L Proctor

We evaluate the robustness of a probabilistic formulation of system identification (ID) to sparse, noisy, and indirect data. Specifically, we compare estimators of future system behavior derived from the Bayesian posterior of a learning…

Machine Learning · Statistics 2023-01-02 Nicholas Galioto , Alex Gorodetsky

The discovery of governing equations from data has been an active field of research for decades. One widely used methodology for this purpose is sparse regression for nonlinear dynamics, known as SINDy. Despite several attempts, noisy and…

Dynamical Systems · Mathematics 2023-09-15 Ali Forootani , Pawan Goyal , Peter Benner