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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…

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

We present a weak formulation and discretization of the system discovery problem from noisy measurement data. This method of learning differential equations from data fits into a new class of algorithms that replace pointwise derivative…

Numerical Analysis · Mathematics 2022-05-03 Daniel A. Messenger , David M. Bortz

We develop a data-driven model discovery and system identification technique for spatially-dependent boundary value problems (BVPs). Specifically, we leverage the sparse identification of nonlinear dynamics (SINDy) algorithm and group…

Computational Engineering, Finance, and Science · Computer Science 2021-07-07 Daniel E. Shea , Steven L. Brunton , J. Nathan Kutz

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

We propose a novel data-driven method called QENDy (Quadratic Embedding of Nonlinear Dynamics) that not only allows us to learn quadratic representations of highly nonlinear dynamical systems, but also to identify the governing equations.…

Dynamical Systems · Mathematics 2025-09-25 Stefan Klus , Joel-Pascal Ntwali N'konzi

At the core of some of the most important problems in plasma physics -- from controlled nuclear fusion to the acceleration of cosmic rays -- is the challenge to describe nonlinear, multi-scale plasma dynamics. The development of reduced…

Plasma Physics · Physics 2022-09-13 E. Paulo Alves , Frederico Fiuza

Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability…

Machine Learning · Computer Science 2021-09-14 Kookjin Lee , Nathaniel Trask , Panos Stinis

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

Atmospheric modeling has recently experienced a surge with the advent of deep learning. Most of these models, however, predict concentrations of pollutants following a data-driven approach in which the physical laws that govern their…

Applications · Statistics 2021-07-08 Javier Rubio-Herrero , Carlos Ortiz Marrero , Wai-Tong Louis Fan

This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy). The algorithm is online in a sense that if performs…

Optimization and Control · Mathematics 2022-03-09 Daniel A. Messenger , Emiliano Dall'Anese , David M. Bortz

Accurately modeling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data.…

Machine Learning · Computer Science 2021-04-28 Kadierdan Kaheman , J. Nathan Kutz , Steven L. Brunton

In this work we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability when tackling real…

Systems and Control · Electrical Eng. & Systems 2024-03-04 Aurelio Raffa Ugolini , Valentina Breschi , Andrea Manzoni , Mara Tanelli

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable…

Other Statistics · Statistics 2022-06-08 Kathleen Champion , Bethany Lusch , J. Nathan Kutz , Steven L. Brunton

Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a…

Systems and Control · Electrical Eng. & Systems 2024-01-03 Sigurd Holmsen , Sølve Eidnes , Signe Riemer-Sørensen

The sparse identification of nonlinear dynamics (SINDy) is a regression framework for the discovery of parsimonious dynamic models and governing equations from time-series data. As with all system identification methods, noisy measurements…

Signal Processing · Electrical Eng. & Systems 2020-10-01 Kadierdan Kaheman , Steven L. Brunton , J. Nathan Kutz

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

Pattern-forming systems can exhibit a diverse array of complex behaviors as external parameters are varied, enabling a variety of useful functions in biological and engineered systems. First-principles derivations of the underlying…

Pattern Formation and Solitons · Physics 2023-11-20 Zachary G. Nicolaou , Guanyu Huo , Yihui Chen , Steven L. Brunton , J. Nathan Kutz

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

Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…

Machine Learning · Computer Science 2023-01-11 Daniel Floryan , Michael D. Graham