fix: fix SDEs with noise dependent on observed variables

Author: AayushSabharwal

src/structural_transformation/symbolics_tearing.jl

@@ -88,6 +88,14 @@ function tearing_sub(expr, dict, s)
     s ? simplify(expr) : expr
 end
 
+function tearing_substitute_expr(sys::AbstractSystem, expr; simplify = false)
+    empty_substitutions(sys) && return expr
+    substitutions = get_substitutions(sys)
+    @unpack subs = substitutions
+    solved = Dict(eq.lhs => eq.rhs for eq in subs)
+    return tearing_sub(expr, solved, simplify)
+end
+
 """
 $(TYPEDSIGNATURES)
 

src/systems/systems.jl

@@ -152,6 +152,8 @@ function __structural_simplify(sys::AbstractSystem, io = nothing; simplify = fal
             noise_eqs = sorted_g_rows
             is_scalar_noise = false
         end
+
+        noise_eqs = StructuralTransformations.tearing_substitute_expr(ode_sys, noise_eqs)
         return SDESystem(full_equations(ode_sys), noise_eqs,
             get_iv(ode_sys), unknowns(ode_sys), parameters(ode_sys);
             name = nameof(ode_sys), is_scalar_noise)

test/sdesystem.jl

@@ -780,3 +780,22 @@ end
     prob = @test_nowarn SDEProblem(sys, nothing, (0.0, 1.0))
     @test_nowarn solve(prob, ImplicitEM())
 end
+
+@testset "Issue#3212: Noise dependent on observed" begin
+    sts = @variables begin
+        x(t) = 1.0
+        input(t)
+        [input = true]
+    end
+    ps = @parameters a = 2
+    @brownian η
+
+    eqs = [D(x) ~ -a * x + (input + 1) * η
+           input ~ 0.0]
+
+    sys = System(eqs, t, sts, ps; name = :name)
+    sys = structural_simplify(sys)
+    @test ModelingToolkit.get_noiseeqs(sys) ≈ [1.0]
+    prob = SDEProblem(sys, [], (0.0, 1.0), [])
+    @test_nowarn solve(prob, RKMil())
+end