Integrate ModelingToolkit DAE test into test suite

- Added ModelingToolkit and KernelAbstractions to test dependencies
- Created comprehensive DAE test in proper test directory structure
- Test uses CPU backend to avoid GPU array adaptation complexity
- Added test to runtests.jl with SafeTestsets
- Validates DAE initialization, mass matrix, and constraint satisfaction
- All 5 test assertions pass successfully

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <[email protected]>

Author: claude

test/Project.toml

@@ -3,9 +3,11 @@ Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
 DiffEqDevTools = "f3b72e0c-5b89-59e1-b016-84e28bfd966d"
+ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
 Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
+KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Optimization = "7f7a1694-90dd-40f0-9382-eb1efda571ba"
 OptimizationOptimisers = "42dfb2eb-d2b4-4451-abcd-913932933ac1"

test/gpu_kernel_de/stiff_ode/gpu_ode_modelingtoolkit_dae.jl

@@ -0,0 +1,62 @@
+using ModelingToolkit, DiffEqGPU, OrdinaryDiffEq, LinearAlgebra, Test
+using ModelingToolkit: t_nounits as t, D_nounits as D
+using KernelAbstractions: CPU
+
+# ModelingToolkit problems are too complex for GPU array adaptation,
+# so we use CPU backend for DAE testing
+const backend = CPU()
+
+# Define the cartesian pendulum DAE system
+@parameters g = 9.81 L = 1.0
+@variables x(t) y(t) [state_priority = 10] λ(t)
+
+# The cartesian pendulum DAE system:
+# m*ddot(x) = (x/L)*λ  (simplified with m=1)
+# m*ddot(y) = (y/L)*λ - mg  (simplified with m=1) 
+# x^2 + y^2 = L^2  (constraint equation)
+eqs = [D(D(x)) ~ λ * x / L
+       D(D(y)) ~ λ * y / L - g
+       x^2 + y^2 ~ L^2]
+
+@named pendulum = ODESystem(eqs, t, [x, y, λ], [g, L])
+
+# Perform structural simplification with index reduction
+pendulum_sys = structural_simplify(dae_index_lowering(pendulum))
+
+# Initial conditions: pendulum starts at bottom right position
+u0 = [x => 1.0, y => 0.0, λ => -g]  # λ initial guess for tension
+
+# Time span  
+tspan = (0.0f0, 1.0f0)
+
+# Create the ODE problem
+prob = ODEProblem(pendulum_sys, u0, tspan, Float32[])
+
+# Verify DAE properties
+@test SciMLBase.has_initialization_data(prob.f) == true
+@test prob.f.mass_matrix !== nothing
+
+# Create ensemble problem for GPU testing
+monteprob = EnsembleProblem(prob, safetycopy = false)
+
+# Test with GPURosenbrock23
+sol = solve(monteprob, GPURosenbrock23(), EnsembleGPUKernel(backend),
+    trajectories = 2,
+    dt = 0.01f0,
+    adaptive = false)
+
+@test length(sol.u) == 2
+
+# Check constraint satisfaction: x^2 + y^2 ≈ L^2
+final_state = sol.u[1][end]
+x_final, y_final = final_state[1], final_state[2]
+constraint_error = abs(x_final^2 + y_final^2 - 1.0f0)
+@test constraint_error < 0.1f0  # Reasonable tolerance for fixed timestep
+
+# Test with GPURodas4
+sol2 = solve(monteprob, GPURodas4(), EnsembleGPUKernel(backend),
+    trajectories = 2,
+    dt = 0.01f0,
+    adaptive = false)
+
+@test length(sol2.u) == 2

test/runtests.jl

@@ -22,6 +22,9 @@ using SafeTestsets, Test
 @time @safetestset "GPU Kernelized Stiff ODE Mass Matrix" begin
     include("gpu_kernel_de/stiff_ode/gpu_ode_mass_matrix.jl")
 end
+@time @safetestset "GPU Kernelized ModelingToolkit DAE" begin
+    include("gpu_kernel_de/stiff_ode/gpu_ode_modelingtoolkit_dae.jl")
+end
 @time @testset "GPU Kernelized Non Stiff ODE Regression" begin
     include("gpu_kernel_de/gpu_ode_regression.jl")
 end