Diagonal noise not detected during lowering of `System` with `@brownian` variables

[AayushSabharwal]

Describe the bug 🐞

Lowering of stochastic systems using @brownian variables does not detect that the noise is diagonal.

Expected behavior

Diagonality is detected and the appropriate solvers are allowed.

Minimal Reproducible Example 👇

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

# Define some variables
@parameters σ ρ β
@variables x(t) y(t) z(t)
@brownian a
eqs = [D(x) ~ σ * (y - x) + 0.1a * x,
    D(y) ~ x * (ρ - z) - y + 0.1a * y,
    D(z) ~ x * y - β * z + 0.1a * z]

@mtkbuild de = System(eqs, t)

u0map = [
    x => 1.0,
    y => 0.0,
    z => 0.0
]

parammap = [
    σ => 10.0,
    β => 26.0,
    ρ => 2.33
]

prob = SDEProblem(de, u0map, (0.0, 100.0), parammap)
sol = solve(prob, SOSRI())

Error & Stacktrace ⚠️

ERROR: The algorithm is not compatible with the chosen noise type. Please see the documentation on the solver methods
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:35
  [2] __init(_prob::SDEProblem{…}, alg::SOSRI, timeseries_init::Vector{…}, ts_init::Vector{…}, ks_init::Type, recompile::Type{…}; saveat::Tuple{}, tstops::Tuple{}, d_discontinuities::Tuple{}, save_idxs::Nothing, save_everystep::Bool, save_noise::Bool, save_on::Bool, save_start::Bool, save_end::Nothing, callback::Nothing, dense::Bool, calck::Bool, dt::Float64, adaptive::Bool, gamma::Rational{…}, abstol::Nothing, reltol::Nothing, qmin::Rational{…}, qmax::Rational{…}, qsteady_min::Int64, qsteady_max::Int64, beta2::Nothing, beta1::Nothing, qoldinit::Rational{…}, controller::Nothing, fullnormalize::Bool, failfactor::Int64, delta::Rational{…}, maxiters::Int64, dtmax::Float64, dtmin::Float64, internalnorm::typeof(DiffEqBase.ODE_DEFAULT_NORM), isoutofdomain::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), unstable_check::typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), verbose::Bool, force_dtmin::Bool, timeseries_errors::Bool, dense_errors::Bool, advance_to_tstop::Bool, stop_at_next_tstop::Bool, initialize_save::Bool, progress::Bool, progress_steps::Int64, progress_name::String, progress_message::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), progress_id::Symbol, userdata::Nothing, initialize_integrator::Bool, seed::UInt64, alias_u0::Bool, alias_jumps::Bool, kwargs::@Kwargs{})
    @ StochasticDiffEq ~/.julia/packages/StochasticDiffEq/tdY4b/src/solve.jl:111
  [3] __solve(prob::SDEProblem{…}, alg::SOSRI, timeseries::Vector{…}, ts::Vector{…}, ks::Nothing, recompile::Type{…}; kwargs::@Kwargs{…})
    @ StochasticDiffEq ~/.julia/packages/StochasticDiffEq/tdY4b/src/solve.jl:6
  [4] solve_call(_prob::SDEProblem{…}, args::SOSRI; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::@Kwargs{})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/Sueu7/src/solve.jl:612
  [5] solve_call(_prob::SDEProblem{…}, args::SOSRI)
    @ DiffEqBase ~/.julia/packages/DiffEqBase/Sueu7/src/solve.jl:569
  [6] solve_up(prob::SDEProblem{…}, sensealg::Nothing, u0::Vector{…}, p::ModelingToolkit.MTKParameters{…}, args::SOSRI; kwargs::@Kwargs{})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/Sueu7/src/solve.jl:1062
  [7] solve_up(prob::SDEProblem{…}, sensealg::Nothing, u0::Vector{…}, p::ModelingToolkit.MTKParameters{…}, args::SOSRI)
    @ DiffEqBase ~/.julia/packages/DiffEqBase/Sueu7/src/solve.jl:1048
  [8] solve(prob::SDEProblem{…}, args::SOSRI; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/Sueu7/src/solve.jl:985
  [9] solve(prob::SDEProblem{…}, args::SOSRI)
    @ DiffEqBase ~/.julia/packages/DiffEqBase/Sueu7/src/solve.jl:975
 [10] top-level scope
    @ REPL[152]:1

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `~/Julia/SciML/ModelingToolkit.jl/TestEnv/Project.toml`
  [4fba245c] ArrayInterface v7.7.1
  [687d7614] ControlSystemsMTK v1.1.0 `../../ControlSystemsMTK.jl`
  [2b5f629d] DiffEqBase v6.147.0
⌅ [06fc5a27] DynamicQuantities v0.11.3
  [f6369f11] ForwardDiff v0.10.36
  [ccbc3e58] JumpProcesses v9.10.1
  [961ee093] ModelingToolkit v9.0.1 `..`
  [16a59e39] ModelingToolkitStandardLibrary v2.4.0 `../../ModelingToolkitStandardLibrary.jl`
⌃ [8913a72c] NonlinearSolve v3.7.1
  [7f7a1694] Optimization v3.22.0 `../../Optimization.jl`
  [fd9f6733] OptimizationMOI v0.4.0 `../../Optimization.jl/lib/OptimizationMOI`
  [36348300] OptimizationOptimJL v0.2.2
  [1dea7af3] OrdinaryDiffEq v6.71.0
  [731186ca] RecursiveArrayTools v3.10.0
  [0bca4576] SciMLBase v2.26.1 `../../SciMLBase.jl`
  [53ae85a6] SciMLStructures v1.1.0
  [860ef19b] StableRNGs v1.0.1
  [9672c7b4] SteadyStateDiffEq v2.0.1
  [789caeaf] StochasticDiffEq v6.65.0
  [2efcf032] SymbolicIndexingInterface v0.3.7
  [d1185830] SymbolicUtils v1.5.0