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Differentiable Models #304

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@FriesischScott

It's time we teach our models to be differentiable. For this we should leverage DifferentiationInterface.jl where possible.

This should work very well for the following models:

  • Model
  • ParallelModel
  • Probably all surrogate models

where we can default to AutoMooncake() because of the way we use DataFrames. When the gradient can not be prepared we can likely fall back to AutoFiniteDifferences().

The ExternalModel is a very different case. We should allow the possibility for extracting gradients if solvers provide them and alternatively use AutoFiniteDifferences().

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