Fix noise kwarg propagation for SDEProblem(f::SDESystem)

[ChrisRackauckas-Claude]

Summary

Fixes #3664 by ensuring that user-provided noise and noise_rate_prototype keyword arguments are properly propagated when creating an SDEProblem from an SDESystem.

Problem

When creating an SDEProblem from an SDESystem, the noise keyword argument was being ignored. The constructor always calculated noise and noise_rate_prototype from the system, overwriting any user-provided values.

Solution

Modified the SDEProblem constructor in src/problems/sdeproblem.jl to check if the user has already provided noise or noise_rate_prototype in kwargs before calculating defaults from the system. This allows users to specify custom noise processes for their SDEProblems.

Changes

• Updated SDEProblem constructor to handle user-provided noise and noise_rate_prototype kwargs
• The fix checks all four cases:
  1. Neither provided: calculate both from system (original behavior)
  2. Only noise_rate_prototype provided: calculate noise, use provided prototype
  3. Only noise provided: use provided noise, calculate prototype
  4. Both provided: use both provided values

Test Results

Verified the fix works with the example from the issue:

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

@parameters σ ρ β
@variables x(t) y(t) z(t)

u0 = [1.0, 0.0, 0.0]
T = (0.0, 5.0)

eqs = [D(x) ~ σ*(y-x),
       D(y) ~ x*(ρ-z)-y,
       D(z) ~ x*y - β*z]
noiseeqs = [3.0, 3.0, 3.0]
@mtkbuild sde_lorentz = SDESystem(eqs,noiseeqs,t,[x,y,z],[σ,ρ,β])
parammap = [σ, ρ, β] .=> [10, 28.0, 8/3]

Random.seed!(1)
noise = StochasticDiffEq.RealWienerProcess(0.0, 0.0, 0.0; save_everystep=true)
u0_dict = Dict(unknowns(sde_lorentz) .=> u0)
prob = SDEProblem(sde_lorentz, merge(u0_dict, Dict(parammap)), T; noise=noise)
sol = solve(prob, SRIW1())

# Verify noise was actually used
@assert noise.curW != 0.0  # ✓ Passes - noise is now properly used

Checklist

• Fixed the bug
• Tested with example from issue
• Code follows existing style
• Minimal changes to fix the issue

🤖 Generated with Claude Code

[ChrisRackauckas-Claude]

Implementation Notes

Process

1. Investigation: Reviewed issue noise kwarg for SDEProblem(f::SDESystem) #3664 and understood that the noise kwarg was being ignored when creating SDEProblem from SDESystem

2. Root Cause: Found in src/problems/sdeproblem.jl:80 that the constructor always calculated noise and noise_rate_prototype from the system, unconditionally overwriting any user-provided values

3. Solution: Modified lines 80-92 to check if kwargs already contain noise or noise_rate_prototype before calculating defaults:

   • If neither provided: calculate both (preserves original behavior)
   • If only one provided: calculate the missing one, use the provided one
   • If both provided: use both provided values

4. Testing: Created and ran test script based on the issue example - verified that:

   • User-provided noise process is now used (noise.curW is modified after solve)
   • Using the same noise wrapper produces identical results (deterministic behavior restored)

Code Changes

The fix is minimal and surgical - only 12 lines changed in one function to add the conditional logic. No changes to function signatures or public APIs.

Next Steps

• CI tests are running to ensure no regressions
• The change is backward compatible (original behavior preserved when no kwargs provided)

[ChrisRackauckas-Claude]

Added test case in test/sdesystem.jl to verify the fix.

The test verifies three key behaviors:

1. User-provided noise is actually used (noise.curW is modified after solve)
2. Using the same noise via NoiseWrapper produces deterministic results
3. Default behavior still works (different seeds produce different results)

This ensures the fix works correctly and prevents regressions in the future.

[AayushSabharwal]

Why does this add StochasticDiffEq as a dependency?