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PySINDy is a Python package for the discovery of governing dynamical systems models from data. In particular, PySINDy provides tools for applying the sparse identification of nonlinear dynamics (SINDy) (Brunton et al. 2016) approach to…

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

The data-driven discovery of dynamics via machine learning is currently pushing the frontiers of modeling and control efforts, and it provides a tremendous opportunity to extend the reach of model predictive control. However, many leading…

Optimization and Control · Mathematics 2019-03-06 Eurika Kaiser , J. Nathan Kutz , Steven L. Brunton

We propose a probabilistic model discovery method for identifying ordinary differential equations (ODEs) governing the dynamics of observed multivariate data. Our method is based on the sparse identification of nonlinear dynamics (SINDy)…

Dynamical Systems · Mathematics 2021-07-06 Seth M. Hirsh , David A. Barajas-Solano , J. Nathan Kutz

Data-driven discovery of partial differential equations (PDEs) offers a promising paradigm for uncovering governing physical laws from observational data. However, in practical scenarios, measurements are often contaminated by noise and…

Machine Learning · Computer Science 2026-03-25 Xingyu Chen , Junxiu An , Jun Guo , Yuqian Zhou

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

SINDy is a method for learning system of differential equations from data by solving a sparse linear regression optimization problem [Brunton et al., 2016]. In this article, we propose an extension of the SINDy method that learns systems of…

Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the…

Dynamical Systems · Mathematics 2021-04-30 Alejandro Carderera , Sebastian Pokutta , Christof Schütte , Martin Weiser

Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology,…

Machine Learning · Computer Science 2025-11-04 G. Pillonetto , A. Giaretta , A. Aravkin , M. Bisiacco , T. Elston

This work is concerned with uncertainty quantification in reduced-order dynamical system identification. Reduced-order models for system dynamics are ubiquitous in design and control applications and recent efforts focus on their…

Systems and Control · Electrical Eng. & Systems 2021-03-10 Prem Ratan Mohan Ram , Ulrich Römer , Richard Semaan

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

Identification of the particle interaction potential is a challenging and important task in dusty plasma, colloids, and smart materials as it allows the characterization of structure formation and helps predict phase transitions. With the…

The Sparse Identification of Nonlinear Dynamics (SINDy) algorithm can be applied to stochastic differential equations to estimate the drift and the diffusion function using data from a realization of the SDE. The SINDy algorithm requires…

Numerical Analysis · Mathematics 2024-01-29 Mathias Wanner , Igor Mezić

Identifying the governing equations of a dynamical system is one of the most important tasks for scientific modeling. However, this procedure often requires high-quality spatio-temporal data uniformly sampled on structured grids. In this…

Machine Learning · Computer Science 2025-05-23 Mars Liyao Gao , J. Nathan Kutz , Bernat Font

Identifying governing equations in physical and biological systems from datasets remains a long-standing challenge across various scientific disciplines, providing mechanistic insights into complex system evolution. Common methods like…

Dynamical Systems · Mathematics 2025-02-28 Mehrdad Anvari , Hamidreza Marasi , Hossein Kheiri

Model parsimony is an important \emph{cognitive bias} in data-driven modelling that aids interpretability and helps to prevent over-fitting. Sparse identification of nonlinear dynamics (SINDy) methods are able to learn sparse…

Machine Learning · Statistics 2025-06-26 Max D. Champneys , Timothy J. Rogers

Distilling physical laws autonomously from data has been of great interest in many scientific areas. The sparse identification of nonlinear dynamics (SINDy) and its variations have been developed to extract the underlying governing…

Systems and Control · Electrical Eng. & Systems 2022-09-08 Adam Purnomo , Mitsuhiro Hayashibe

We develop an efficient and robust high-dimensional sparse Fourier algorithm for noisy samples. Earlier in the paper ``Multi-dimensional sublinear sparse Fourier algorithm" (2016), an efficient sparse Fourier algorithm with $\Theta(ds \log…

Numerical Analysis · Mathematics 2019-07-09 Bosu Choi , Andrew Christlieb , Yang Wang

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

We study the Gaussian Process regression model in the context of training data with noise in both input and output. The presence of two sources of noise makes the task of learning accurate predictive models extremely challenging. However,…

Machine Learning · Statistics 2015-07-03 Cuong Tran , Vladimir Pavlovic , Robert Kopp