Video Abstracts | Kutz Research Group

Deep learning models for global coordinate transformations that linearize PDEs

This video highlights recent innovations for using neural networks for discovery of linearizing Koopman transformations for dynamics in complex systems.
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Data-driven Discovery of Governing Equations

This video highlights recent innovations for the targeted use of neural networks for discovery coordinates and dynamics in complex systems.
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Deep Learning of Hiearchical Multiscale Differential Equation Time Steppers

This video highlights how deep learning can be used to produce stable, multiscale time-stepping schemes.
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Data-driven Stabilization of Periodic Orbits

This video highlights how to stabilise periodic orbits using modern data-driven methods
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Deep Learning of Dynamics and Coordinates with SINDy Autoencoders

This video highlights recent innovations for discovering coordinates and dynamics jointly using deep learning
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PySINDy: A Python Library for Model Discovery

This video highlights an open source python package for model discovery
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From Fourier to Koopman: Spectral Methods for Forecasting

This video highlights recent innovations for long-time forecasting
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Models for Rotating Detonation Engines (RDEs)

This video highlights recent innovations for characterizing the detonation dynamics of rotating detonation engines
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Data-driven Discovery of Governing Equations

This video highlights recent innovations for discovering nonlinear dynamical systems from time series data.
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Data-driven sensor placement methods

This video highlights highlights data-driven methods and dimensionality reduction for optimal sensor placement.
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K. Manohar, B. Brunton, J. N. Kutz and S. L. Brunton, Data-Driven Sparse Sensor Placement, arxiv (2016)

Sparse identification of insect wing strain

This video highlights methods for exploiting sparsity on insect wing strain signals for downstream environmental identification.
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K. Manohar, S. L. Brunton, and J. N. Kutz Environment identification in flight using sparse approximation of wing strain, Journal of Fluids and Structures 70 (2017) 162-180.

Data-driven discovery of partial differential equations

This video highlights extensions of our sparse identification for nonlinear dynamical systems (SINDy) to partial differential equations.
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S. Rudy, J. L. Proctor, S. L. Brunton, and J. N. Kutz Data-driven discovery of partial differential equations, arxiv (2016)

Data-driven methods for discovery of observables and Koopman embeddings in dynamical systems

This video highlights a presentation at the IPAM workshop on Collective Variables in Classical Mechanics (Workshop II from October 24-28, 2016).
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Primary collaborators Steven Brunton and Joshua Proctor

Hankel Alternative View of Koopman (HAVOK) Analysis

This video highlights a new algorithm to decompose chaos into a linear system with intermitting forcing.
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S. Brunton, B. Brunton, J. L. Proctor, E. Kaiser and J. N. Kutz Chaos as an intermittently forced linear system, arxiv (2016)

Sparse Sensor Placement Optimization for Classification (SSPOC)

This video highlights the new innovations around using sparsity promoting techniques for determining optimal sensor placement.
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B. Brunton, S. Brunton, J. L. Proctor and J. N. Kutz Sparse sensor placement optimization for classification, arxiv (2013)

Generalizing Koopman Theory to Allow for Inputs and Control

This video highlights the new innovations around Koopman theory and data-driven control strategies.
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J. L. Proctor, S. L. Brunton and J. N. Kutz Generalizing Koopman theory to allow for inputs and control, arxiv (2016)

Dynamic Mode Decomposition with Control

This video highlights the concepts of Dynamic Mode Decomposition which includes actuation and control.
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J. L. Proctor, S. L. Brunton and J. N. Kutz Dynamic Mode Decomposition with Control, SIAM Journal of Applied Dynamical Systems 15 (2016) 142-161

Inferring biological networks by sparse idendification of nonlinear dynamics

This video highlights the concepts of sparse regression for identifying nonlinear dynamical systems that are of the form dy/dt=f(y)/g(y) which often arise in biological networks.
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N. M. Mangam, S. L. Brunton, J. L. Proctor and J. N. Kutz Inferring biological networks by sparse identification of nonlinear dynamics, arxiv (2016)

Koopman theory for partial differential equations

This video highlights the concepts of Koopman theory and how they can be used for partial differential equations.
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J. N. Kutz, J. Proctor and S. L. Brunton, Koopman theory for partial differential equations, arxiv (2016).

Online interpolation point refinement for reduced order models using a genetic algorithm

This video highlights the use of a genetic algorithm for optimizing interpolation approximations in nonlinear model reduction.
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S. Sargsyan, S. L. Brunton & J. N. Kutz, Online interpolation point refinement for reduced order models using a genetic algorithm, arxiv (2016).

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

This video highlights the recent innovation of using overcomplete libraries and sparse regression to discover nonlinear dynamical systems from time series data.
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S. Brunton, J. Proctor and J. N. Kutz, Discovering governing equations from data by sparse identification of nonlinear dynamical systems, Proceedings of the National Academy of Sciences (2016).

Koopman observable subspaces and finite linear representations of nonlinear dynamical systems for control

This video highlights the recent innovation of Koopman analysis for representing nonlinear systems and control.
[Part 1], [Part 2], [Part 3]

S. L. Brunton, B. Brunton, J. L. Proctor and J. N. Kutz, Koopman observable subspaces and finite linear representations of nonlinear dynamical systems for control PLOS ONE (2016)

Nonlinear Model Reduction for Dynamical Systems using Sparse Optimal Sensor Locations from Learned Nonlinear Libraries

This video highlights the recent innovation of library learning architecture with the DEIMS method on reduced order models.
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S. Sargsyan, S. Brunton and J. N. Kutz, Nonlinear model reduction for dynamical systems using sparse sensor locations from learned libraries, Physical Review E 92 (2015) 033304.

Multi-Resolution Dynamic Mode Decomposition

This video highlights the recent innovation of multi-resolution analysis applied to dynamic mode decomposition.
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J. N. Kutz, X. Fu and S. L. Brunton, Multi-resolution dynamic mode decomposition SIAM Journal of Applied Dynamical Systems 15 (2016) 713-735

What is a Koopman Mode?

This video highlights how one might define a Koopman Mode.
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Arxiv paper: There is no research article available at the current time

Helping Communicate Research Ideas to the Broader Community

Deep learning models for global coordinate transformations that linearize PDEs

Data-driven Discovery of Governing Equations

Deep Learning of Hiearchical Multiscale Differential Equation Time Steppers

Data-driven Stabilization of Periodic Orbits

Deep Learning of Dynamics and Coordinates with SINDy Autoencoders

PySINDy: A Python Library for Model Discovery

From Fourier to Koopman: Spectral Methods for Forecasting

Models for Rotating Detonation Engines (RDEs)

Data-driven Discovery of Governing Equations

Data-driven sensor placement methods

Sparse identification of insect wing strain

Data-driven discovery of partial differential equations

Data-driven methods for discovery of observables and Koopman embeddings in dynamical systems

Hankel Alternative View of Koopman (HAVOK) Analysis

Sparse Sensor Placement Optimization for Classification (SSPOC)

Generalizing Koopman Theory to Allow for Inputs and Control

Dynamic Mode Decomposition with Control

Inferring biological networks by sparse idendification of nonlinear dynamics

Koopman theory for partial differential equations

Online interpolation point refinement for reduced order models using a genetic algorithm

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

Koopman observable subspaces and finite linear representations of nonlinear dynamical systems for control

Nonlinear Model Reduction for Dynamical Systems using Sparse Optimal Sensor Locations from Learned Nonlinear Libraries

Multi-Resolution Dynamic Mode Decomposition

What is a Koopman Mode?