NonlinearSolveBase: mark nonlinear-solve algorithms Enzyme-inactive

[ChrisRackauckas-Claude]

Please ignore until reviewed by @ChrisRackauckas. Draft, opened by an agent.

What

Declare the whole AbstractNonlinearSolveAlgorithm hierarchy Enzyme.EnzymeRules.inactive_type, in NonlinearSolveBaseEnzymeExt:

Enzyme.EnzymeRules.inactive_type(::Type{<:NonlinearSolveBase.AbstractNonlinearSolveAlgorithm}) = true

Why

When a NonlinearProblem is solved under Enzyme.set_runtime_activity(Reverse) — most notably the ModelingToolkit DAE-initialization solve reached through get_initial_values → solve_up — the default NonlinearSolvePolyAlgorithm arrives at the solve_up custom Enzyme rule as a positional args.... Nonlinear-solve algorithms are pure solver configuration (Vals, Rationals, Nothing/Missing sentinels, nested immutable sub-algorithms, and a ForwardDiff tag type parameter) with no differentiable floating-point data, but without an inactivity declaration set_runtime_activity promotes that configuration argument to Duplicated. That manifests, nondeterministically, as either:

• the roots_activep (DFT_CONSTANT) != activep (DFT_DUP_ARG) assertion inside Enzyme's enzyme_custom_setup_args, or
• a spurious algorithm shadow that corrupts activity bookkeeping for the genuinely-active u0/p, silently dropping a cotangent component.

Marking the algorithm hierarchy inactive forces Const, so activep == roots_activep == DFT_CONSTANT. This mirrors the established, shipping pattern in SciMLBase (inactive_type(::Type{<:AbstractSensitivityAlgorithm})) and LinearSolve (inactive_type(::Type{<:SciMLLinearSolveAlgorithm})).

This is type-safe (the abstract supertype covers the polyalg wrapper, every nested member algorithm, and the bare-algorithm case) and semantically exact (algorithms are never a differentiation target — gradients flow only through prob/u0/p). It is precompile-safe: a more-specific method on an already-loaded EnzymeRules.inactive_type, no parent-module method overwritten.

Context

This is the NonlinearSolveBase half of getting Enzyme reverse-mode AD to work on the outside of an MTK DAE solve (the within_autodiff wrap-skip and the inactive_kwarg for the solve_up rule are already merged). A downstream SciMLSensitivity PR will flip the corresponding mtk.jl test on and bump its lower bound once this is tagged.

Test

Adds lib/NonlinearSolveBase/test/enzyme_inactive_algorithm.jl (wired into runtests.jl), a deterministic regression test that the declaration covers AbstractNonlinearSolveAlgorithm, the concrete NonlinearSolvePolyAlgorithm, and does not touch unrelated differentiable types.

Verified locally (Julia 1.11, NonlinearSolveBase dev'd from this branch + Enzyme/ChainRulesCore to trigger the extension):

NonlinearSolveBase 2.30.2
Test Summary:                                                       | Pass  Total  Time
Enzyme inactive_type covers the nonlinear-solve algorithm hierarchy |    4      4  0.2s

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