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Symbolic Regression (SR) is a widely studied field of research that aims to infer symbolic expressions from data. A popular approach for SR is the Sparse Identification of Nonlinear Dynamical Systems (SINDy) framework, which uses sparse…

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 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 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

The moment quantities associated with the nonlinear Schrodinger equation offer important insights towards the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment…

Pattern Formation and Solitons · Physics 2024-06-10 Su Yang , Shaoxuan Chen , Wei Zhu , P. G. Kevrekidis

System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods. Addressing the intricate challenges of…

Machine Learning · Computer Science 2024-12-17 Arunabh Singh , Joyjit Mukherjee

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 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

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…

Understanding and predicting complex dynamics in accelerators is necessary for their successful operation. A grand challenge in accelerator physics is to develop predictive virtual accelerators that mitigate design cost and schedule risk.…

Accelerator Physics · Physics 2024-10-21 Liam A. Pocher , Irving Haber , Thomas M. Antonsen , Patrick G. O'Shea

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

Sparse identification of nonlinear dynamics (SINDy) is a data-driven framework for estimating classical nonlinear dynamical systems from time-series data. In this approach, system dynamics is represented as a linear combination of a…

Quantum Physics · Physics 2026-02-17 Yusei Tateyama , Yuzuru Kato

The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. In this paper, we argue that this makes SINDy a potentially useful tool for causal discovery and that existing…

Machine Learning · Computer Science 2023-01-02 Andrew O'Brien , Rosina Weber , Edward Kim

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

Inferring the structure and dynamics of network models is critical to understanding the functionality and control of complex systems, such as metabolic and regulatory biological networks. The increasing quality and quantity of experimental…

Dynamical Systems · Mathematics 2016-05-27 Niall M. Mangan , Steven L. Brunton , Joshua L. Proctor , J. Nathan Kutz

Recent progress in autoencoder-based sparse identification of nonlinear dynamics (SINDy) under $\ell_1$ constraints allows joint discoveries of governing equations and latent coordinate systems from spatio-temporal data, including simulated…

Machine Learning · Computer Science 2022-11-22 L. Mars Gao , J. Nathan Kutz

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

Many dynamical systems exhibit oscillatory behavior that can be modeled with differential equations. Recently, these equations have increasingly been derived through data-driven methods, including the transparent technique known as Sparse…

Adaptation and Self-Organizing Systems · Physics 2024-07-03 Bartosz Prokop , Nikita Frolov , Lendert Gelens

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

In this paper, we give an in-depth error analysis for surrogate models generated by a variant of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an overview of a variety of non-linear system identification…

Numerical Analysis · Mathematics 2024-09-21 Benjamin Russo , M. Paul Laiu