Symbolic indexing getters return wrong indices for DAEProblem

[ChrisRackauckas-Claude]

Description

When using symbolic indexing with a DAEProblem, the getters (prob[x], prob[y]) return values from the wrong indices in the underlying u0 array. The setters work correctly, but the getters are swapped.

Minimal Working Example

using ModelingToolkit, SciMLBase
using ModelingToolkit: t_nounits as t, D_nounits as D

@variables x(t) [guess = 1.0] y(t) [guess = 1.0]
@parameters p = missing [guess = 1.0] q = missing [guess = 1.0]
@mtkbuild sys = ODESystem([D(x) ~ p * y + q * t, x^3 + y^3 ~ 5], t; 
    initialization_eqs = [p^2 + q^2 ~ 3])

# Create the DAE problem
prob = DAEProblem{true}(sys, [D(x) => cbrt(4), D(y) => -1 / cbrt(4), p => 1.0], (0.0, 0.4))

println("Initial state:")
println("  unknowns(sys) = ", unknowns(sys))  # [y(t), x(t)] - note the order
println("  prob.u0 = ", prob.u0)  # [1.0, 1.0]
println("  prob[x] = ", prob[x])  # 1.0
println("  prob[y] = ", prob[y])  # 1.0

# Set values using symbolic indexing
prob[x] = 1.0
prob[y] = cbrt(4)  # ≈ 1.587

println("\nAfter setting prob[x]=1.0 and prob[y]=cbrt(4):")
println("  prob[x] = ", prob[x])  # Returns 1.0 (expected: 1.0) ✓
println("  prob[y] = ", prob[y])  # Returns 1.587... (expected: 1.587...) ✓
println("  prob.u0 = ", prob.u0)  # [1.587..., 1.0]

println("\n🔴 BUG: The values are swapped in u0!")
println("  prob.u0[1] = ", prob.u0[1], " (should be y = ", prob[y], ")")
println("  prob.u0[2] = ", prob.u0[2], " (should be x = ", prob[x], ")")

Analysis

The unknowns are ordered as [y(t), x(t)] in the system, so:

• u0[1] corresponds to y(t)
• u0[2] corresponds to x(t)

When we set values:

• prob[x] = 1.0 correctly sets u0[2] = 1.0 ✓
• prob[y] = cbrt(4) correctly sets u0[1] = cbrt(4) ✓

But when we get values:

• prob[x] incorrectly returns u0[1] instead of u0[2] ✗
• prob[y] incorrectly returns u0[2] instead of u0[1] ✗

Impact

This bug causes test failures in Sundials.jl when using CheckInit with DAEProblems, as the initialization checks read the wrong values through symbolic indexing.

Environment

• Julia: 1.11.6
• ModelingToolkit.jl: 10.22.0
• SciMLBase.jl: 2.119.0
• SymbolicIndexingInterface.jl: 0.3.43

Related

This was discovered while working on SciML/Sundials.jl#503