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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
- S. Brunton, J. Proctor, J. Kutz
- Computer ScienceProceedings of the National Academy of Sciences
- 11 September 2015
This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning and using sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data.
On dynamic mode decomposition: Theory and applications
A theoretical framework in which dynamic mode decomposition is defined as the eigendecomposition of an approximating linear operator, which generalizes DMD to a larger class of datasets, including nonsequential time series, and shows that under certain conditions, DMD is equivalent to LIM.
Data-driven discovery of partial differential equations
The sparse regression method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation.
Dynamic mode decomposition - data-driven modeling of complex systems
This first book to address the DMD algorithm presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development, and blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses.
Modal Analysis of Fluid Flows: An Overview
The intent of this document is to provide an introduction to modal analysis that is accessible to the larger fluid dynamics community and presents a brief overview of several of the well-established techniques.
Deep learning for universal linear embeddings of nonlinear dynamics
It is often advantageous to transform a strongly nonlinear system into a linear one in order to simplify its analysis for prediction and control, so the authors combine dynamical systems with deep learning to identify these hard-to-find transformations.
Chaos as an intermittently forced linear system
- S. Brunton, Bingni W. Brunton, J. Proctor, E. Kaiser, J. Kutz
- PhysicsNature Communications
- 18 August 2016
A universal, data-driven decomposition of chaos as an intermittently forced linear system is presented, combining delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates.
Dynamic Mode Decomposition with Control
This work develops a new method which extends dynamic mode decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems and provides the additional innovation of being able to disambiguate between the underlying dynamics and the effects of actuation, resulting in accurate input-output models.
Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns
- K. Manohar, Bingni W. Brunton, J. Kutz, S. Brunton
- Computer ScienceIEEE Control Systems
- 26 January 2017
This article explores how to design optimal sensor locations for signal reconstruction in a framework that scales to arbitrarily large problems, leveraging modern techniques in machine learning and sparse sampling.