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Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may…

Machine Learning · Computer Science 2024-11-06 Jianke Yang , Wang Rao , Nima Dehmamy , Robin Walters , Rose Yu

Discovering symbolic differential equations from data uncovers fundamental dynamical laws underlying complex systems. However, existing methods often struggle with the vast search space of equations and may produce equations that violate…

Machine Learning · Computer Science 2026-03-11 Jianke Yang , Manu Bhat , Bryan Hu , Yadi Cao , Nima Dehmamy , Robin Walters , Rose Yu

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

Machine Learning · Computer Science 2021-11-17 Zhao Chen , Yang Liu , Hao Sun

The Sparse Identification of Nonlinear Dynamics (SINDy) framework is a robust method for identifying governing equations, successfully applied to ordinary, partial, and stochastic differential equations. In this work we extend SINDy to…

Numerical Analysis · Mathematics 2024-12-19 Alessandro Pecile , Nicola Demo , Marco Tezzele , Gianluigi Rozza , Dimitri Breda

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

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…

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

Data-driven discovery of governing equations has advanced significantly in recent years; however, existing methods often struggle in multiscale systems where dynamically significant terms may have small coefficients. Therefore, we propose…

Machine Learning · Computer Science 2026-04-21 Zhenhua Dang , Lei Zhang , Long Wang , Guowei He

Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…

Computational Physics · Physics 2019-10-31 Bing Xiong , Haiyang Fu , Feng Xu , Yaqiu Jin

The discovery of governing differential equations from data is an open frontier in machine learning. The sparse identification of nonlinear dynamics (SINDy) \citep{brunton_discovering_2016} framework enables data-driven discovery of…

Machine Learning · Computer Science 2023-10-10 Mozes Jacobs , Bingni W. Brunton , Steven L. Brunton , J. Nathan Kutz , Ryan V. Raut

The sparse identification of nonlinear dynamical systems (SINDy) is a data-driven technique employed for uncovering and representing the fundamental dynamics of intricate systems based on observational data. However, a primary obstacle in…

Dynamical Systems · Mathematics 2025-09-23 Ali Forootani , Harshit Kapadia , Sridhar Chellappa , Pawan Goyal , Peter Benner

The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. In this paper, we argue that this makes SINDy a potentially useful tool for causal discovery and that existing…

Machine Learning · Computer Science 2023-01-02 Andrew O'Brien , Rosina Weber , Edward Kim

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

Identifying from observation data the governing differential equations of a physical dynamics is a key challenge in machine learning. Although approaches based on SINDy have shown great promise in this area, they still fail to address a…

Machine Learning · Computer Science 2025-10-22 Fayad Ali Banna , Antoine Caradot , Eduardo Brandao , Jean-Philippe Colombier , Rémi Emonet , Marc Sebban

Data driven discovery of partial differential equations (PDEs) is a promising approach for uncovering the underlying laws governing complex systems. However, purely data driven techniques face the dilemma of balancing search space with…

Machine Learning · Computer Science 2025-05-12 Hao Xu , Yuntian Chen , Rui Cao , Tianning Tang , Mengge Du , Jian Li , Adrian H. Callaghan , Dongxiao Zhang

Domain decomposition provides an effective way to tackle the dilemma of physics-informed neural networks (PINN) which struggle to accurately and efficiently solve partial differential equations (PDEs) in the whole domain, but the lack of…

Machine Learning · Computer Science 2024-04-30 Ye Liu , Jie-Ying Li , Li-Sheng Zhang , Lei-Lei Guo , Zhi-Yong Zhang

Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system discovery that has been shown to successfully recover governing dynamical systems from data (Brunton et al., PNAS, '16; Rudy et al., Sci. Adv. '17). Recently, several…

Numerical Analysis · Mathematics 2021-07-28 Daniel A. Messenger , David M. Bortz

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

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…

Equation discovery methods hold promise for extracting knowledge from physics-related data. However, existing approaches often require substantial prior information that significantly reduces the amount of knowledge extracted. In this…

Neural and Evolutionary Computing · Computer Science 2025-01-28 Mikhail Maslyaev , Alexander Hvatov
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