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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…

Deep learning has shown strong potential in modeling complex spatiotemporal dynamics. However, most existing methods depend on densely and uniformly sampled data, which is often unavailable in practice due to sensor and cost limitations. In…

Machine Learning · Computer Science 2025-12-16 Han Wan , Qi Wang , Yuan Mi , Rui Zhang , Hao Sun

The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…

Machine Learning · Computer Science 2025-07-30 Rahul Golder , M. M. Faruque Hasan

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

Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when…

Machine Learning · Computer Science 2024-12-13 Paul Ghanem , Ahmet Demirkaya , Tales Imbiriba , Alireza Ramezani , Zachary Danziger , Deniz Erdogmus

A general framework for recovering drift and diffusion dynamics from sampled trajectories is presented for the first time for stochastic delay differential equations. The core relies on the well-established SINDy algorithm for the sparse…

Numerical Analysis · Mathematics 2025-08-06 Dimitri Breda , Dajana Conte , Raffaele D'Ambrosio , Ida Santaniello , Muhammad Tanveer

Structural monitoring for complex built environments often suffers from mismatch between design, laboratory testing, and actual built parameters. Additionally, real-world structural identification problems encounter many challenges. For…

Machine Learning · Computer Science 2022-08-29 Xuyang Li , Hamed Bolandi , Talal Salem , Nizar Lajnef , Vishnu Naresh Boddeti

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

Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification of nonlinear dynamics (SINDy) framework, powered by heuristic…

Machine Learning · Computer Science 2022-06-02 Dimitris Bertsimas , Wes Gurnee

Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…

Machine Learning · Computer Science 2023-03-02 Rui Wang , Rose Yu

There is growing interest in using machine learning (ML) methods for structural metamodeling due to the substantial computational cost of traditional simulations. Purely data-driven strategies often face limitations in model robustness,…

Applied Physics · Physics 2024-04-30 R. Bailey Bond , Pu Ren , Jerome F. Hajjar , Hao Sun

This paper investigates the applicability of a recently-proposed nonlinear sparse Bayesian learning (NSBL) algorithm to identify and estimate the complex aerodynamics of limit cycle oscillations. NSBL provides a semi-analytical framework…

Computational Engineering, Finance, and Science · Computer Science 2022-10-24 Rimple Sandhu , Brandon Robinson , Mohammad Khalil , Chris L. Pettit , Dominique Poirel , Abhijit Sarkar

Nonlinear dynamics is ubiquitous in nature and commonly seen in various science and engineering disciplines. Distilling analytical expressions that govern nonlinear dynamics from limited data remains vital but challenging. To tackle this…

Artificial Intelligence · Computer Science 2023-02-03 Fangzheng Sun , Yang Liu , Jian-Xun Wang , Hao Sun

Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…

Machine Learning · Computer Science 2025-11-17 Zitong Zhang , Hao Sun

Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools for applying the…

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

With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying the evolution of these systems. However, the existing…

Machine Learning · Statistics 2021-02-03 Yang Li , Jinqiao Duan

In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…

Machine Learning · Statistics 2021-02-17 Hao Xu , Haibin Chang , Dongxiao Zhang

In order to extract governing equations from time-series data, various approaches are proposed. Among those, sparse identification of nonlinear dynamics (SINDy) stands out as a successful method capable of modeling governing equations with…

Signal Processing · Electrical Eng. & Systems 2024-06-07 Jinho Choi

To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…

Computational Physics · Physics 2021-05-04 Gert-Jan Both , Georges Tod , Remy Kusters