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Given an approximate model (obtained by theoretical simplifications etc.), how can observations (data) be used to fine tune it?. Standard supervised learning techniques can used for constructing models between dependent and independent variables but it seems like that having some prior knowledge should help.

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  • $\begingroup$ I would make an augmented model, where some learner predicts the difference between the pristine/theoretical/false simple model and the noisy/practical/real actual world. This would allow you to move the work of the learner away from having to approximate the simple model first, and accelerate convergence and make sure that for the same complexity the combined answers have better accuracy (or other general performance depending on your error metric). $\endgroup$ Mar 15, 2018 at 15:17

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"it seems like having some prior knowledge should help"

Well, you can encode that into your description of the model, no? If you expect some variables to be squared, etc, you can make that a parameter of the model.

But if you mean, is there a way to start with a perfect (theoretical) model and build out from there, one way to do it would be to build a preliminary model using a perfect dataset (i.e. one built using the exact function that your model is based on). Then you can use some kind of update functionality to add new data to the model to "tune" it. The size of the theoretical dataset would determine how susceptible your model is to change under the new data. Hope this answers your question.

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