Matrix ODE gradient tests fail with all reverse-mode AD backends

[ChrisRackauckas-Claude]

Description

The Matrix Multiplication ODE gradient tests fail with all reverse-mode AD backends (ReverseDiff, Tracker, Zygote) on all Julia versions.

Test Location

test/concrete_solve_derivatives.jl - "Matrix Multiplication ODE" testset

Current Status

Tests are marked as @test_broken in the test suite.

Test Code

@testset "Matrix Multiplication ODE" begin
    solvealg_test = Tsit5()
    sensealg_test = InterpolatingAdjoint()
    tspan = (0.0, 1.0)
    u0_mat = rand(4, 8)
    p0 = rand(16)
    f_aug(u, p, t) = reshape(p, 4, 4) * u

    function loss_mat(p)
        prob = ODEProblem(f_aug, u0_mat, tspan, p; alg = solvealg_test, sensealg = sensealg_test)
        sol = solve(prob)
        return sum(sol[:, :, end])
    end

    # These tests fail for ReverseDiff, Tracker, and Zygote
    res2 = grad_fn(loss_mat, p0)
    res4 = grad_fn(loss_mat2, p0)
    @test res2 ≈ res4 atol = 1.0e-10
    @test res2 ≈ ForwardDiff.gradient(loss_mat, p0) atol = 1.0e-10
end

Related

This issue was identified during the AD backend test refactoring in PR #1322.