Zygote AD example disabled in documentation due to IntegralSolution adjoint issue

[ChrisRackauckas-Claude]

Summary

The Zygote.jl example in the documentation (docs/src/tutorials/differentiating_integrals.md) has been changed to a non-executable code block because Zygote.gradient fails with:

Need an adjoint for constructor SciMLBase.IntegralSolution{...}

This was done in PR #299 to fix the documentation build.

Error Details

When running:

using Integrals, Zygote
f(x, p) = sum(sin.(x .* p))
domain = (ones(2), 3ones(2))
p = ones(2)

function testf(p)
    prob = IntegralProblem(f, domain, p)
    sin(solve(prob, HCubatureJL(), reltol = 1e-6, abstol = 1e-6)[1])
end

Zygote.gradient(testf, p)  # Fails

The error indicates that Zygote needs a constructor adjoint for IntegralSolution that is either missing or not being loaded correctly.

Related Issues

• Issue AD tests disabled on Julia pre-release due to Zygote.jl incompatibilities #297 - AD tests disabled on Julia pre-release due to Zygote.jl incompatibilities
• broken nested forward diff on julia v1.12 FluxML/Zygote.jl#1594, #1591, #1580 - Upstream Zygote issues

Action Items

• Investigate why the IntegralSolution adjoint is not working
• Re-enable the Zygote example in documentation once fixed

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