Notes30July.tex

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\section{Model Error}

Model error vs. observation error?\\

Satellite example\\


model the radiance? direct observation:\\
then observation simple\\

model the temperature? indirect observation:\\
what's the error of the inverse problem\\

The different models make different dynamics.\\

Linear model nonlinear H, reverse, both nonlinear?\\

\section{Hurricane Prediction}
Parameter depends on the location / time.\\

Augmenting system? \\

Dynamics, attracting fixed pts, bistable dynamics\\

Sensitivity to the time when the observations are made?\\
Rapid Change Occurs?

\section{DA in adaptive mesh}

$\dot{u}_i=F(\{u_i\}),\dot{x}_i=G(\{x_i\},\{u_i\})$

Sea ice model.\\

AM to solve pde's\\

change rapidly some points, finer?\\

Augment the mesh variables, double the size; physical model\\

Fix a reference mesh, project the ensembles to this mesh.\\

Point: very little work in adaptive mesh; the model of DA is really the computational model\\

Comparison made on different grids?? Mean and covariance? Apples and oranges?\\

\section{Dimension Reduction}
Decomposition between slow and fast compositions => two systems\\
Strongly negative and positive Lyaponov exponents\\

Lower the dimension, project the observations to the reduced space.\\

Dynamically split the model without a priori knowing how to.\\

Lyaponov vectors?\\

pdf in high dimension, concentrated in the center? Sample? \\

Connection between dynamics of the problem and the pdf?\\

Diffusion maps???\\

\section{Machine Learning}






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