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I'm guessing they use something like Gaussian noise with a width approx. equal to the uncertainty in the initial conditions.



"Bred vectors" are an example: https://en.wikipedia.org/wiki/Bred_vector

Note that these vectors are generated not by just sampling the uncertainty in I.C.'s. Of course, this is because the space of I.C. perturbations is too high-dimensional to cover. In the method above, selection of perturbation direction is based on the adjustments implied when new data is sync'ed to the model.

There are other techniques.




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