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The accurate forecasting of complex, high-dimensional dynamical systems from observational data is a fundamental task across numerous scientific and engineering disciplines. A significant challenge arises from noise-corrupted measurements,…

Machine Learning · Computer Science 2026-04-14 Xuyang Li , John Harlim , Dibyajyoti Chakraborty , Romit Maulik

We introduce an equation learning framework to identify a closed set of equations for moment quantities in 1D thermal radiation transport (TRT) in optically thin media. While optically thick media admits a well-known diffusive closure, the…

Dynamical Systems · Mathematics 2025-10-15 Daniel Messenger , Ben Southworth , Hans Hammer , Luis Chacon

The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based…

Computational Physics · Physics 2024-10-31 Marcus Haywood-Alexander , Giacomo Arcieri , Antonios Kamariotis , Eleni Chatzi

We consider the problem of system identification of partially observed linear time-invariant (LTI) systems. Given input-output data, we provide non-asymptotic guarantees for identifying the system parameters under general heavy-tailed noise…

Systems and Control · Electrical Eng. & Systems 2025-04-28 Vinay Kanakeri , Aritra Mitra

Many studies on acoustic radiation forces focus on characterizing the behavior of acoustic fields. However, the dynamic response of objects, particularly those larger than the wavelength, remains underexplored. Here we bridge this gap by…

Chaotic Dynamics · Physics 2025-08-06 Mehdi Akbarzadeh , Ben Halkon , Sebastian Oberst

Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…

Machine Learning · Computer Science 2021-05-18 Fangzheng Sun , Yang Liu , Hao Sun

The quantitative formulation of evolution equations is the backbone for prediction, control, and understanding of dynamical systems across diverse scientific fields. Besides deriving differential equations for dynamical systems based on…

Data Analysis, Statistics and Probability · Physics 2025-01-06 Tim W. Kroll , Oliver Kamps

Data normalisation, a common and often necessary preprocessing step in engineering and scientific applications, can severely distort the discovery of governing equations by magnitudebased sparse regression methods. This issue is…

Machine Learning · Computer Science 2026-03-06 Jay Raut , Daniel N. Wilke , Stephan Schmidt

We evaluate the robustness of a probabilistic formulation of system identification (ID) to sparse, noisy, and indirect data. Specifically, we compare estimators of future system behavior derived from the Bayesian posterior of a learning…

Machine Learning · Statistics 2023-01-02 Nicholas Galioto , Alex Gorodetsky

This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…

Optimization and Control · Mathematics 2015-04-27 Wei Pan , Ye Yuan , Jorge Gonçalves , Guy-Bart Stan

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…

Sparse Identification of Nonlinear Dynamics (SINDy) has become a standard methodology for inferring governing equations of dynamical systems from observed data using statistical modeling. However, classical SINDy approaches rely on…

Methodology · Statistics 2025-07-24 Aliaksandr Hubin

The Weak-form Estimation of Non-linear Dynamics (WENDy) framework is a recently developed approach for parameter estimation and inference of systems of ordinary differential equations (ODEs). Prior work demonstrated WENDy to be robust,…

Machine Learning · Computer Science 2025-10-24 Nic Rummel , Daniel A. Messenger , Stephen Becker , Vanja Dukic , David M. Bortz

The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse…

Applications · Statistics 2017-02-07 Yong Huang , James L. Beck , Hui Li

We present a pragmatic approach to the sparse identification of nonlinear dynamics for systems with discrete delays. It relies on approximating the underlying delay model with a system of ordinary differential equations via pseudospectral…

Dynamical Systems · Mathematics 2024-08-06 Enrico Bozzo , Dimitri Breda , Muhammad Tanveer

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

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

Power grid parameter estimation involves the estimation of unknown parameters, such as inertia and damping coefficients, using observed dynamics. In this work, we present a comparison of data-driven algorithms for the power grid parameter…

Systems and Control · Electrical Eng. & Systems 2021-07-09 Subhash Lakshminarayana , Saurav Sthapit , Carsten Maple

The identification of governing equations for dynamical systems is everlasting challenges for the fundamental research in science and engineering. Machine learning has exhibited great success to learn and predict dynamical systems from…

Optimization and Control · Mathematics 2022-09-27 Zhongshun Shi , Hang Ma , Hoang Tran , Guannan Zhang

This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying results…

Numerical Analysis · Mathematics 2023-02-09 Pongpisit Thanasutives , Takashi Morita , Masayuki Numao , Ken-ichi Fukui