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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

A general framework for recovering drift and diffusion dynamics from sampled trajectories is presented for the first time for stochastic delay differential equations. The core relies on the well-established SINDy algorithm for the sparse…

Numerical Analysis · Mathematics 2025-08-06 Dimitri Breda , Dajana Conte , Raffaele D'Ambrosio , Ida Santaniello , Muhammad Tanveer

Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of…

Numerical Analysis · Mathematics 2022-05-04 Urban Fasel , J. Nathan Kutz , Bingni W. Brunton , Steven L. Brunton

The sparse identification of nonlinear dynamics (SINDy) has been established as an effective method to learn interpretable models of dynamical systems from data. However, for high-dimensional slow-fast dynamical systems, the regression…

Dynamical Systems · Mathematics 2025-07-02 Diemen Delgado-Cano , Erick Kracht , Urban Fasel , Benjamin Herrmann

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

In order to extract governing equations from time-series data, various approaches are proposed. Among those, sparse identification of nonlinear dynamics (SINDy) stands out as a successful method capable of modeling governing equations with…

Signal Processing · Electrical Eng. & Systems 2024-06-07 Jinho Choi

Recent advances in the field of data-driven dynamics allow for the discovery of ODE systems using state measurements. One approach, known as Sparse Identification of Nonlinear Dynamics (SINDy), assumes the dynamics are sparse within a…

Dynamical Systems · Mathematics 2023-06-14 Jacqueline Wentz , Alireza Doostan

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

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

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

The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. However, SINDy assumes the user has prior knowledge of the variables in the system and of a function library that…

Machine Learning · Computer Science 2024-01-25 Andrew O'Brien

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

In this paper, we address the challenge of deriving dynamical models from sparse and noisy data. High-quality data is crucial for symbolic regression algorithms; limited and noisy data can present modeling challenges. To overcome this, we…

Machine Learning · Computer Science 2024-10-14 Junette Hsin , Shubhankar Agarwal , Adam Thorpe , Luis Sentis , David Fridovich-Keil

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

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

The sparse identification of nonlinear dynamics (SINDy) approach can discover the governing equations of dynamical systems based on measurement data, where the dynamical model is identified as the sparse linear combination of the given…

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

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

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

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