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What would we need to become backend independent via using DifferentiationInterface? #1040

@oxinabox

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@oxinabox

This is a space for a discussion on what would be required to change here and in DifferentiationInterface to make this package backend agnostic.
(it equally could have been made on DifferentiationInterface.jl but I had to pick a location)

I had thought we were a fair way away from that, but i see DifferentiationInterface is already supporting caches and is using ADTypes.

Very likely this would still be a breaking change for SciMLSensitivity, but hopefully not a major one.
I think it would probably be worth it.
@ChrisRackauckas once referred to SciMLSensitivity as "the final boss of julia", because it depends on so many packages. Including ones like Enzyme and Zygote which are sensitive to changes to julias internals, and which sometimes break during precompilation because of this, which makes SciMLSensitivity break on nightly even if you are not using those packages.

cc @gdalle

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