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The idea is that you learn a model by calculating the derivative of free energy with respect to your model parameters.

Yes, but you have to specify a generative model (or at least put boundaries to it). Then you learn params of that model.

I was talking about learning the model structure also.

Some attempts have been made in the form of Bayesian model reduction [1].

The idea is to 'carve' out the structure of your model using free energy minimization.