Helping Communicate Research Ideas to the Broader Community

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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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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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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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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

 

 

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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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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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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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Dynamic Mode Decomposition with Control

 

This video highlights the concepts of Dynamic Mode Decomposition which includes actuation and control.
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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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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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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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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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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.
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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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Multi-Resolution Dynamic Mode Decomposition

 

This video highlights the recent innovation of multi-resolution analysis applied to dynamic mode decomposition.
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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
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