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Fitting differential equations to Darwin anomalies

Hello Paul and Hello everyone

This is a rather kiddish attempt to start fitting differential equations to the Darwin Anomalies:

CDF

Fitting Differential Equations to Darwin Anomalies

PDF

Fitting Differential...

The ideas were unearthed during the earlier forecast algorithms which I posted here and the wavelet scalograms showing the 3 months period for Darwin Delta Anomalies.

The parameter for the differential equations are picked kinda arbitrarily to experiment. But later on there will be an algorithm that generates them. I wish to use Machine Learning algorithms to forecast them, then use them to solve differential equations, as opposed to Machine Learning algorithms forecast do the entire data. Needs much more thought and coding.

Dara

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    Oh parameter e = 0 which makes the 1st order and 0th order equations to have same solutions. Change e to see how they behave differently.

    Dara

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    CDF document has live code in it, so it is solving the differential equations on the fly as the sliders are manipulated. So there is no hardwired or fudged equations.

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    Dara, Looks good.
    This is my one sentence synopsis. First attempt only features 1st derivatives, which gives it the flavor of a nonlinear dragged response, and with only stable solutions as a result.

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    I added some more code:

    1. (a, e, d) cube was turned into a grid
    2. At each node of the grid a differential equation was formed and solved
    3. squared-sum of the error between the solution from the diff EQ in #2 and original Darwin Delta Anomalies computed
    4. Min was performed all over the grid and the smallest squared sum for error was found

    1-4 takes a few minutes for total 1700 such grid points. This is brute force, I could divide this grid to sub-grids and run each on a different cpu.

    Hit a glitch with Differential Evolution instead of this brute force, a programming issue, so much faster algorithms are available. Submitted a ticked for TechSupport at Wolfram to help out.

    However generally speaking, I feel a lot better fitting a differential equation to a time-series data, find the min squared-sum candidate for best fit.

    Now the challenge is to extract ideas from John and Paul on differential equation candidates, larger orders, and on volumetric data. To my eyes all equations are created equal, until I code them :)

    Feeling a lot better...

    Dara

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