Data Driven Modeling
&
Scientific Computation

Data-Driven Modeling & Scientific Computation

Lecture 1

 

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[ Part 1 ] [ Part 2 ]

 
Dynamic Mode Decomposition: This lecture provides an introduction to the Dynamic Mode Decomposition (DMD). The focus is on approximating a nonlinear dynamical system with a linear system.

 

MATLAB CODE

Lecture 2

 

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[ view ]

 
Koopman Theory: This lecture generalizes the DMD method to a function of the state-space, thus potentially providing a coordinate system that is intrinsically linear.

 

Lecture 3

 

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[ view ]

 
Time-Delay Embeddings: This lecture generalizes the Koopman/DMD method to a function of the state-space created by time-delay embedding of the dynamical trajectories.

 

MATLAB CODE

 

 

KEY REFERENCES AND SUPPLEMENTARY VIDEOS

 

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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.
[Part 1], [Part 2], [Part 3]

 

 

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Dynamic Mode Decomposition with Control

 

This video highlights the concepts of Dynamic Mode Decomposition which includes actuation and control.
[View]

 

 

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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.
[View]

 

 

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Multi-Resolution Dynamic Mode Decomposition

 

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

 

 

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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.
[View]

 

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