Data Driven Modeling
&
Scientific Computation

Dimensionality Reduction for PDEs

Lecture 1

 

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BASIS SELECTION AND IDEAL MODES: This lecture provides an introduction to basis representations, POD modes, and orthogonality of function spaces.

 

MATLAB COMMANDS

FFT

Lecture 2

 

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SPECIAL FUNCTIONS + GALERKIN PROJECTIONS: The harmonic oscillator is considered along with its ideal basis functions: the Gauss-Hermite polynomials.

 

MATLAB COMMANDS

SVD

Lecture 3

 

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POD EXPANSION : We construct a ROM model of the nonlinear Schrodinger equation using a 2 POD mode expansion.

 

MATLAB COMMANDS

ODE45

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