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Many model selection algorithms rely on sparse dictionary learning to provide interpretable and physics-based governing equations. The optimization algorithms typically use a hard thresholding process to enforce sparse activations in the…

Optimization and Control · Mathematics 2025-04-30 Derek W. Jollie , Scott G. McCalla

Nonlinear system identification often involves a fundamental trade-off between interpretability and flexibility, often requiring the incorporation of physical constraints. We propose a unified data-driven framework that combines the…

Machine Learning · Computer Science 2025-09-16 Federico J. Gonzalez , Luis P. Lara

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

We develop a weak-form sparse identification method for interacting particle systems (IPS) with the primary goals of reducing computational complexity for large particle number $N$ and offering robustness to either intrinsic or extrinsic…

Machine Learning · Statistics 2022-07-20 Daniel A. Messenger , David M. Bortz

Implicit Neural Representations (INRs) are increasingly recognized as a versatile data modality for representing discretized signals, offering benefits such as infinite query resolution and reduced storage requirements. Existing signal…

Machine Learning · Computer Science 2025-03-26 Dhananjaya Jayasundara , Sudarshan Rajagopalan , Yasiru Ranasinghe , Trac D. Tran , Vishal M. Patel

Poincar\'e maps are an integral aspect to our understanding and analysis of nonlinear dynamical systems. Despite this fact, the construction of these maps remains elusive and is primarily left to simple motivating examples. In this…

Dynamical Systems · Mathematics 2020-04-10 Jason J. Bramburger , J. Nathan Kutz

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

In this work, we revisit dictionary-based sparse regression, in particular, Sequential Threshold Least Squares (STLS), and propose a score-guided library selection to provide practical guidance for data-driven modeling, with emphasis on…

Machine Learning · Statistics 2025-12-17 Hangjun Cho , Fabio V. G. Amaral , Andrei A. Klishin , Cassio M. Oishi , Steven L. Brunton

Sparse system identification of nonlinear dynamic systems is still challenging, especially for stiff and high-order differential equations for noisy measurement data. The use of highly correlated functions makes distinguishing between true…

Computational Physics · Physics 2025-12-19 Ashish Pal , Sutanu Bhowmick , Satish Nagarajaiah

This work focuses on the issue of variable selection in functional regression. Unlike most work in this framework, our approach does not select isolated points in the definition domain of the predictors, nor does it rely on the expansion of…

Statistics Theory · Mathematics 2018-03-05 Victor Picheny , Rémi Servien , Nathalie Villa-Vialaneix

Extrapolative prediction of complex nonlinear dynamics remains a central challenge in engineering. This study proposes a one-shot learning method to identify global frequency-response curves from a single excitation time history by learning…

Machine Learning · Computer Science 2026-04-17 Teng Ma , Luca Rosafalco , Wei Cui , Lin Zhao , Attilio Frangi

Air pollution, particularly particulate matter (PM2.5), poses significant risks to public health and the environment, necessitating accurate prediction and continuous monitoring for effective air quality management. However, air quality…

Machine Learning · Computer Science 2024-09-19 Yohan Choi , Boaz Choi , Jachin Choi

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

Sparsity is a ubiquitous feature of many real world signals such as natural images and neural spiking activities. Conventional compressed sensing utilizes sparsity to recover low dimensional signal structures in high ambient dimensions…

Statistics Theory · Mathematics 2018-07-02 Abbas Kazemipour

Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…

Chaotic Dynamics · Physics 2020-08-19 Jason J. Bramburger , Daniel Dylewsky , J. Nathan Kutz

Predicting the human burden of vector-borne diseases from limited surveillance data remains a major challenge, particularly in the presence of nonlinear transmission dynamics and delayed effects arising from vector ecology and human…

Dynamical Systems · Mathematics 2026-02-20 Dimitri Breda , Muhammad Tanveer , Jianhong Wu , Xue Zhang

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

Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…

Machine Learning · Computer Science 2022-10-18 Luning Sun , Daniel Zhengyu Huang , Hao Sun , Jian-Xun Wang

Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations…

Dynamical Systems · Mathematics 2020-01-29 Patrick A. K. Reinbold , Daniel R. Gurevich , Roman O. Grigoriev

This work leverages laser vibrometry and the weak form of the sparse identification of nonlinear dynamics (WSINDy) for partial differential equations to learn macroscale governing equations from full-field experimental data. In the…

Numerical Analysis · Mathematics 2024-10-01 Abigail C. Schmid , Alireza Doostan , Fatemeh Pourahmadian