feat: use observed equations for guesses of observed variables

src/systems/nonlinear/initializesystem.jl

@@ -165,7 +165,16 @@ function generate_initializesystem(sys::ODESystem;
         [p for p in parameters(sys) if !haskey(paramsubs, p)]
     )
 
-    eqs_ics = Symbolics.substitute.([eqs_ics; observed(sys)], (paramsubs,))
+    # 7) use observed equations for guesses of observed variables if not provided
+    obseqs = observed(sys)
+    for eq in obseqs
+        haskey(defs, eq.lhs) && continue
+        any(x -> isequal(default_toterm(x), eq.lhs), keys(defs)) && continue
+
+        defs[eq.lhs] = eq.rhs
+    end
+
+    eqs_ics = Symbolics.substitute.([eqs_ics; obseqs], (paramsubs,))
     vars = [vars; collect(values(paramsubs))]
     for k in keys(defs)
         defs[k] = substitute(defs[k], paramsubs)

test/initializationsystem.jl

@@ -836,3 +836,11 @@ end
     integ = init(prob, Rosenbrock23())
     @test integ[y] ≈ -0.5
 end
+
+@testset "Use observed equations for guesses of observed variables" begin
+    @variables x(t) y(t) [state_priority = 100]
+    @mtkbuild sys = ODESystem(
+        [D(x) ~ x + t, y ~ 2x + 1], t; initialization_eqs = [x^3 + y^3 ~ 1])
+    isys = ModelingToolkit.generate_initializesystem(sys)
+    @test isequal(defaults(isys)[y], 2x + 1)
+end