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I have some functional, such as S[f] = \int_\Omega f^2(x) dx. If you're familiar with physics, it's the action. This object takes in a function defined on a certain domain \Omega and gives you a number. The math jargon for this is functional.

Now I need to minimize this thing with respect to f. I know SciPy has an optimize package that allows one to minimize multivariable functions, but I am curious if there is a better way considering if I used this I would be minimizing over ~10,000 variables (because the functions are essentially just lists of 10,000 numbers).

Do I have any other options?

Nate Stemen
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2 Answers2

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You could use symbolic regression to find the function. There are several packages available:

Here is a good paper on symbolic regression by Schmidt and Lipson.

Ohjeah
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Although it is more designed for doing Neural Network stuff, Tensorflow sounds like it would work for you. It has the ability to differentiate vector equations and also optimize them using gradient descent.

Alex Shmakov
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