Avoid ForwardDiff Jacobians for GPU steady-state adjoints

[ChrisRackauckas-Claude]

Please ignore this draft until it has been reviewed by @ChrisRackauckas.

What changed and why

DeepEquilibriumNetworks overrides SciMLSensitivity's automatic steady-state sense-algorithm choice, but its override left autodiff=true for GPU states. ForwardDiff 1.4.4 began zeroing the unused tail of chunked dual arrays with scalar indexing, so constructing the steady-state adjoint Jacobian now fails on CuArray.

Select autodiff=false only when the steady-state problem's initial state is an AbstractGPUArray, matching SciMLSensitivity's own GPU-specific choice while preserving ForwardDiff Jacobians for CPU states. GPUArraysCore moves from a test extra to a direct dependency because runtime dispatch now uses its public AbstractGPUArray interface.

Regression boundary

The current main failure resolves ForwardDiff 1.4.5 and SciMLSensitivity 7.119.0, then errors in ForwardDiff._seed_zero_partials! with Scalar indexing is disallowed:

• failing main run: https://github.com/SciML/DeepEquilibriumNetworks.jl/actions/runs/32990908259
• failing GPU job: https://github.com/SciML/DeepEquilibriumNetworks.jl/actions/runs/32990908259/job/98277422908

The previous GPU run resolved ForwardDiff 1.4.3 and SciMLSensitivity 7.116.2; its dense steady-state adjoint cases cleared this error before the job later failed in an unrelated V100 cuDNN convolution:

• previous run: https://github.com/SciML/DeepEquilibriumNetworks.jl/actions/runs/30374833857
• previous GPU job: https://github.com/SciML/DeepEquilibriumNetworks.jl/actions/runs/30374833857/job/90328502950

ForwardDiff 1.4.4 introduced the chunk-tail zeroing path:

• release: https://github.com/JuliaDiff/ForwardDiff.jl/releases/tag/v1.4.4
• implementation PR: Unseed only the chunk, and split unseed! out of seed! JuliaDiff/ForwardDiff.jl#821

There were no repository GPU runs between those dependency resolutions, so the resolved dependency boundary, rather than a DeepEquilibriumNetworks commit, is the narrowest available boundary.

Verification

Failing before the source fix, with the new regression test present:

steady-state sensitivity defaults: Test Failed at test/utils_tests.jl:48
  Expression: DEQs.default_sensealg(gpu_prob) isa SteadyStateAdjoint{0, false}
   Evaluated: SciMLSensitivity.SteadyStateAdjoint{0, true, ...} isa
              SciMLSensitivity.SteadyStateAdjoint{0, false}

Test Summary:                       | Pass  Fail  Total   Time
Utils Tests                         |   14     1     15  59.8s
  steady-state sensitivity defaults |    1     1      2   3.5s
ERROR: Some tests did not pass: 14 passed, 1 failed, 0 errored, 0 broken.

Passing after the fix:

$ GROUP=Core julia +release --project=. -e 'using Pkg; Pkg.resolve(); Pkg.test()'
Test Summary: | Pass  Total   Time
Utils Tests   |   15     15  58.2s
Test Summary: | Pass  Total      Time
Layers Tests  | 1538   1538  26m27.2s
Testing DeepEquilibriumNetworks tests passed

$ GROUP=QA julia +release --project=. -e 'using Pkg; Pkg.test()'
Test Summary: | Pass  Total     Time
QA            |   20     20  2m03.6s
Testing DeepEquilibriumNetworks tests passed

The following also exited successfully with no output:

julia +release -m Runic --inplace src/DeepEquilibriumNetworks.jl src/utils.jl test/utils_tests.jl
typos Project.toml src/DeepEquilibriumNetworks.jl src/utils.jl test/utils_tests.jl
git diff --check

GPUArraysCore is MIT-licensed, compatible with this MIT-licensed package.

GPU CI classification

The PR's GPU job completed with 578 passes and 48 errors. None of the remaining errors follows the path changed here:

• The clean-base failure uses ForwardDiff.Tag{SciMLBase.UDerivativeWrapper...} while constructing SteadyStateAdjointProblem. The PR job has zero UDerivativeWrapper occurrences, and the new default-sense-algorithm regression passes 15/15.
• Twelve errors use ForwardDiff.Tag{SciMLBase.NonlinearFunction...} in the forward solve. They come from the pre-existing test configuration NewtonRaphson(; autodiff=AutoForwardDiff(; chunksize=12)), introduced in a30d8f1, and are independent of the default adjoint selected by this PR.
  A separate focused repair changes that explicit GPU Newton configuration to AutoFiniteDiff() in Use finite differences for GPU Newton tests #244; it is intentionally not mixed into this adjoint fix.
• Thirty-six errors are CUDNN_STATUS_EXECUTION_FAILED_CUDART from NNlib/cuDNN forward convolutions in untouched layer and test code. The clean-base job stopped at the original adjoint error before reaching those later cases; the base and PR jobs nevertheless resolve identical GPUArraysCore, Lux, LuxCUDA, NNlib, CUDA, cuDNN, and JLL versions.

GPU job: https://github.com/SciML/DeepEquilibriumNetworks.jl/actions/runs/33104383320/job/98635451731

Not verified locally

This host has no CUDA-capable GPU. The regression test verifies the CPU/GPU dispatch decision using an AbstractGPUArray test double; the GPU conclusions above come from the clean-base and PR CI logs. Documentation was not built because this does not change public API or documentation.

Related documentation fix

The clean-main DEQs documentation failure is addressed separately in #245.

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