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Related papers: Mesh-free sparse identification of nonlinear dynam…

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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

We propose a three-tier machine learning framework based on the next-generation Equation-Free algorithm for learning the spatio-temporal dynamics of mass-constrained complex systems with hidden states, whose dynamics can in principle be…

Numerical Analysis · Mathematics 2026-02-10 Gianmaria Viola , Alessandro Della Pia , Lucia Russo , Ioannis Kevrekidis , Constantinos Siettos

This paper introduces the Parsimonious Dynamic Mode Decomposition (parsDMD), a novel algorithm designed to automatically select an optimally sparse subset of dynamic modes for both spatiotemporal and purely temporal data. By incorporating…

Methodology · Statistics 2024-12-02 Arpan Das , Pier Marzocca , Oleg Levinski

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

Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom.…

Pattern Formation and Solitons · Physics 2022-12-05 Sheikh Saqlain , Wei Zhu , Efstathios G. Charalampidis , Panayotis G. Kevrekidis

Atmospheric modeling has recently experienced a surge with the advent of deep learning. Most of these models, however, predict concentrations of pollutants following a data-driven approach in which the physical laws that govern their…

Applications · Statistics 2021-07-08 Javier Rubio-Herrero , Carlos Ortiz Marrero , Wai-Tong Louis Fan

The recent focus on the efficiency of deep neural networks (DNNs) has led to significant work on model compression approaches, of which weight pruning is one of the most popular. At the same time, there is rapidly-growing computational…

Machine Learning · Computer Science 2022-08-25 Elias Frantar , Dan Alistarh

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

Dynamical systems can confront one of two extreme types of disturbances: persistent zero-mean independent noise, and sparse nonzero-mean adversarial attacks, depending on the specific scenario being modeled. While mean-based estimators like…

Optimization and Control · Mathematics 2026-03-31 Jihun Kim , Javad Lavaei

We develop a principled mathematical framework for controlling nonlinear, networked dynamical systems. Our method integrates dimensionality reduction, bifurcation theory and emerging model discovery tools to find low-dimensional subspaces…

Dynamical Systems · Mathematics 2020-06-24 Megan Morrison , J. Nathan Kutz

Scientific machine learning for inferring dynamical systems combines data-driven modeling, physics-based modeling, and empirical knowledge. It plays an essential role in engineering design and digital twinning. In this work, we primarily…

Machine Learning · Computer Science 2024-01-09 Pawan Goyal , Igor Pontes Duff , Peter Benner

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

Sparse sensor placement is a central challenge in the efficient characterization of complex systems when the cost of acquiring and processing data is high. Leading sparse sensing methods typically exploit either spatial or temporal…

Optimization and Control · Mathematics 2022-06-08 Thomas L. Mohren , Thomas L. Daniel , Steven L. Brunton , Bingni W. Brunton

Identifying network dynamics is a critical yet challenging task to to understand the mechanism of real-world social systems. There are two types of algorithms, and one requires the knowledge of self-dynamics function, interactive function,…

Social and Information Networks · Computer Science 2026-05-21 Mingyu Kang , Jianxi Gao , Wenwu Yu , Linyuan Lv

State estimation is required whenever we deal with high-dimensional dynamical systems, as the complete measurement is often unavailable. It is key to gaining insight, performing control or optimizing design tasks. Most deep learning-based…

Machine Learning · Computer Science 2022-03-15 Yash Kumar , Souvik Chakraborty

A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the…

Systems and Control · Electrical Eng. & Systems 2023-07-19 Xiaolong He , Youngsoo Choi , William D. Fries , Jon Belof , Jiun-Shyan Chen

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

Machine learning (ML) and artificial intelligence (AI) algorithms are now being used to automate the discovery of physics principles and governing equations from measurement data alone. However, positing a universal physical law from data…

Machine Learning · Computer Science 2021-02-23 Brian M. de Silva , David M. Higdon , Steven L. Brunton , J. Nathan Kutz

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

Obtaining predictive low-order models is a central challenge in fluid dynamics. Data-driven frameworks have been widely used to obtain low-order models of aerodynamic systems; yet, resulting models tend to yield predictions that grow…