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

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.

This fix checks 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.

Fixes #3664

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

Co-Authored-By: Claude <noreply@anthropic.com>

Author: ChrisRackauckas

Project.toml

@@ -58,6 +58,7 @@ SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0"
 SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
 SymbolicUtils = "d1185830-fcd6-423d-90d6-eec64667417b"
 Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"

src/problems/sdeproblem.jl

@@ -77,7 +77,20 @@ end
         t = tspan !== nothing ? tspan[1] : tspan, check_length, eval_expression,
         eval_module, check_compatibility, sparse, expression, kwargs...)
 
-    noise, noise_rate_prototype = calculate_noise_and_rate_prototype(sys, u0; sparsenoise)
+    # Only calculate noise and noise_rate_prototype if not provided by user
+    if !haskey(kwargs, :noise) && !haskey(kwargs, :noise_rate_prototype)
+        noise, noise_rate_prototype = calculate_noise_and_rate_prototype(sys, u0; sparsenoise)
+    elseif !haskey(kwargs, :noise)
+        noise, _ = calculate_noise_and_rate_prototype(sys, u0; sparsenoise)
+        noise_rate_prototype = kwargs[:noise_rate_prototype]
+    elseif !haskey(kwargs, :noise_rate_prototype)
+        _, noise_rate_prototype = calculate_noise_and_rate_prototype(sys, u0; sparsenoise)
+        noise = kwargs[:noise]
+    else
+        noise = kwargs[:noise]
+        noise_rate_prototype = kwargs[:noise_rate_prototype]
+    end
+
     kwargs = process_kwargs(sys; expression, callback, eval_expression, eval_module,
         op, kwargs...)