Solutions Are Seldom Chaotic

Chaotic Data (Lorenz equations)

Solution of model equations

Chaotic Data

(Lorenz equations)

Solution of model equations

Time

0

200

x

20

-20

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Best attempt to fit previous equation to data from the Lorenz attractor

Uses Principal Component Analysis

(AKA: Singular Value Decomposition)

Good short-term prediction (optimized for that)

Bad long-term prediction (seldom chaotic)

More complicated models don't help