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We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…

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

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…

Methodology · Statistics 2022-01-27 Christos Merkatas , Simo Särkkä

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…

Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this…

Systems and Control · Computer Science 2017-12-01 Zhe Bai , Eurika Kaiser , Joshua L. Proctor , J. Nathan Kutz , Steven L. Brunton

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

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 growing integration of renewable energy sources has significantly reduced grid inertia, making modern power systems more vulnerable to instabilities. Accurate estimation of dynamic parameters such as inertia constants and damping…

Dynamical Systems · Mathematics 2025-12-08 Aiman Mushtaq Purra , Danish Rafiq

Seismic data often undergoes severe noise due to environmental factors, which seriously affects subsequent applications. Traditional hand-crafted denoisers such as filters and regularizations utilize interpretable domain knowledge to design…

Signal Processing · Electrical Eng. & Systems 2023-04-21 Zitai Xu , Yisi Luo , Bangyu Wu , Deyu Meng

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

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

We introduce the dynamics mode decomposition for monitoring wide-area power grid networks from sparse measurement data. The mathematical framework fuses data from multiple sensors based on multivariate statistics, providing accurate full…

Pattern Formation and Solitons · Physics 2019-06-11 J. Jorge Ramos , J. Nathan Kutz

Discovering governing equations from observational data remains a fundamental challenge in scientific modeling, particularly when the underlying mathematical structure is unknown. Traditional sparse identification methods like SINDy excel…

Machine Learning · Computer Science 2026-05-12 Mohammad Amin Basiri , Charles Nicholson

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

Denoising score matching (DSM) provides a way to learn data distributions by training a neural network to recover the score function, defined as the gradient of the log density, from noise-corrupted samples. Once trained, the score…

Machine Learning · Computer Science 2026-05-11 Victor Livernoche , Jie Zan , Reihaneh Rabbany

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…

Numerical Analysis · Mathematics 2021-02-15 Zhiming Zhang , Yongming Liu

Supervised training for real-world denoising presents challenges due to the difficulty of collecting large datasets of paired noisy and clean images. Recent methods have attempted to address this by utilizing unpaired datasets of clean and…

Computer Vision and Pattern Recognition · Computer Science 2025-03-28 Hamadi Chihaoui , Paolo Favaro

The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development…

Dynamical Systems · Mathematics 2016-04-27 Steven L. Brunton , Joshua L. Proctor , J. Nathan Kutz

Dynamic mode decomposition (DMD) provides a practical means of extracting insightful dynamical information from fluids datasets. Like any data processing technique, DMD's usefulness is limited by its ability to extract real and accurate…

Fluid Dynamics · Physics 2016-03-23 Scott T. M. Dawson , Maziar S. Hemati , Matthew O. Williams , Clarence W. Rowley

Physical computing has the potential to enable widespread embodied intelligence by leveraging the intrinsic dynamics of complex systems for efficient sensing, processing, and interaction. While individual devices provide basic data…