What comes on top of a generator of a PDE?

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Summary:

Are there mathematical methods above the calculus of variations, finding as solutions types of variations.
From some principles in nature we are using in physics the calculus of variations. Let me call it a generator for PDE's. My question: Are there levels above? What I mean is: Is there mathematics where you have principles where the solutions are generators for the generators for PDEs ?
What about generators for the generators for the generators?
 

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