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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

Rapid evolution of sensor technology, advances in instrumentation, and progress in devising data-acquisition softwares/hardwares are providing vast amounts of data for various complex phenomena, ranging from those in atomospheric…

Computational Engineering, Finance, and Science · Computer Science 2023-05-04 Muhammad Sahimi

Machine learning (ML) is redefining what is possible in data-intensive fields of science and engineering. However, applying ML to problems in the physical sciences comes with a unique set of challenges: scientists want physically…

Computational Physics · Physics 2020-07-06 Kathleen Champion , Peng Zheng , Aleksandr Y. Aravkin , Steven L. Brunton , J. Nathan Kutz

Discovering governing equations from data is crucial for understanding complex systems in many diverse fields from science to engineering. Yet, there still is a lack of versatile computational toolbox to deal with this long standing…

Chaotic Dynamics · Physics 2026-05-15 Chengzuo Zhuge , Zheng Jiang , Zhefan Xu , Wei Chen

Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques…

Machine Learning · Computer Science 2023-05-04 Kevin Egan , Weizhen Li , Rui Carvalho

Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology,…

Machine Learning · Computer Science 2025-11-04 G. Pillonetto , A. Giaretta , A. Aravkin , M. Bisiacco , T. Elston

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

Methodology · Statistics 2022-09-08 Joshua S. North , Christopher K. Wikle , Erin M. Schliep

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

The value of unknown parameters of multibody systems is crucial for prediction, monitoring, and control, sometimes estimated using a biased physics-based model leading to incorrect outcomes. Discovering motion equations of multibody systems…

Computational Engineering, Finance, and Science · Computer Science 2022-10-24 Ehsan Askari , Guillaume Crevecoeur

Often the underlying system of differential equations driving a stochastic dynamical system is assumed to be known, with inference conditioned on this assumption. We present a Bayesian framework for discovering this system of differential…

Methodology · Statistics 2021-01-13 Kushagra Gupta , Dootika Vats , Snigdhansu Chatterjee

With the advent of modern data collection and storage technologies, data-driven approaches have been developed for discovering the governing partial differential equations (PDE) of physical problems. However, in the extant works the model…

Machine Learning · Statistics 2019-05-28 Haibin Chang , Dongxiao Zhang

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

With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics…

Machine Learning · Statistics 2018-04-18 Lorenzo Boninsegna , Feliks Nüske , Cecilia Clementi

Many natural systems exhibit chaotic behaviour such as the weather, hydrology, neuroscience and population dynamics. Although many chaotic systems can be described by relatively simple dynamical equations, characterizing these systems can…

Dynamical Systems · Mathematics 2022-06-15 H. Ribera , S. Shirman , A. V. Nguyen , N. M. Mangan

The discovery of governing equations from data has been an active field of research for decades. One widely used methodology for this purpose is sparse regression for nonlinear dynamics, known as SINDy. Despite several attempts, noisy and…

Dynamical Systems · Mathematics 2023-09-15 Ali Forootani , Pawan Goyal , Peter Benner

Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…

Numerical Analysis · Mathematics 2020-03-02 A. Goeßmann , M. Götte , I. Roth , R. Sweke , G. Kutyniok , J. Eisert

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

Dynamical Systems · Mathematics 2023-05-17 Nan Chen , Yinling Zhang

Distilling analytical models from data has the potential to advance our understanding and prediction of nonlinear dynamics. Although discovery of governing equations based on observed system states (e.g., trajectory time series) has…

Machine Learning · Computer Science 2021-06-10 Lele Luan , Yang Liu , Hao Sun

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

Discovering governing equations from data, in particular high dimensional data, is challenging in various fields of science and engineering, and it has potential to revolutionise the science and technology in this big data era. This paper…

Fluid Dynamics · Physics 2024-01-12 X. Lin , D. Xiao , F. Fang