Merge pull request #3440 from AayushSabharwal/as/ode-to-nonlinear

feat: allow `NonlinearSystem(::ODESystem)` and `NonlinearProblem(::ODESystem)`

Author: ChrisRackauckas

src/systems/nonlinear/nonlinearsystem.jl

@@ -232,6 +232,32 @@ function NonlinearSystem(eqs; kwargs...)
     return NonlinearSystem(eqs, collect(allunknowns), collect(new_ps); kwargs...)
 end
 
+"""
+    $(TYPEDSIGNATURES)
+
+Convert an `ODESystem` to a `NonlinearSystem` solving for its steady state (where derivatives are zero).
+Any differential variable `D(x) ~ f(...)` will be turned into `0 ~ f(...)`. The returned system is not
+simplified. If the input system is `complete`d, then so will the returned system.
+"""
+function NonlinearSystem(sys::AbstractODESystem)
+    eqs = equations(sys)
+    obs = observed(sys)
+    subrules = Dict(D(x) => 0.0 for x in unknowns(sys))
+    eqs = map(eqs) do eq
+        fast_substitute(eq, subrules)
+    end
+
+    nsys = NonlinearSystem(eqs, unknowns(sys), [parameters(sys); get_iv(sys)];
+        parameter_dependencies = parameter_dependencies(sys),
+        defaults = merge(defaults(sys), Dict(get_iv(sys) => Inf)), guesses = guesses(sys),
+        initialization_eqs = initialization_equations(sys), name = nameof(sys),
+        observed = obs)
+    if iscomplete(sys)
+        nsys = complete(nsys; split = is_split(sys))
+    end
+    return nsys
+end
+
 function calculate_jacobian(sys::NonlinearSystem; sparse = false, simplify = false)
     cache = get_jac(sys)[]
     if cache isa Tuple && cache[2] == (sparse, simplify)
@@ -529,6 +555,10 @@ function DiffEqBase.NonlinearProblem{iip}(sys::NonlinearSystem, u0map,
     return remake(NonlinearProblem{iip}(f, u0, p, pt; filter_kwargs(kwargs)...))
 end
 
+function DiffEqBase.NonlinearProblem(sys::AbstractODESystem, args...; kwargs...)
+    NonlinearProblem(NonlinearSystem(sys), args...; kwargs...)
+end
+
 """
 ```julia
 DiffEqBase.NonlinearLeastSquaresProblem{iip}(sys::NonlinearSystem, u0map,

test/nonlinearsystem.jl

@@ -390,3 +390,53 @@ end
     @test !any(isequal(p[1]), parameters(sys))
     @test is_parameter(sys, p)
 end
+
+@testset "Can convert from `ODESystem`" begin
+    @variables x(t) y(t)
+    @parameters p q r
+    @named sys = ODESystem([D(x) ~ p * x^3 + q, 0 ~ -y + q * x - r], t;
+        defaults = [x => 1.0, p => missing], guesses = [p => 1.0],
+        initialization_eqs = [p^3 + q^3 ~ 4r], parameter_dependencies = [r ~ 3p])
+    nlsys = NonlinearSystem(sys)
+    defs = defaults(nlsys)
+    @test length(defs) == 3
+    @test defs[x] == 1.0
+    @test defs[p] === missing
+    @test isinf(defs[t])
+    @test length(guesses(nlsys)) == 1
+    @test guesses(nlsys)[p] == 1.0
+    @test length(initialization_equations(nlsys)) == 1
+    @test length(parameter_dependencies(nlsys)) == 1
+    @test length(equations(nlsys)) == 2
+    @test all(iszero, [eq.lhs for eq in equations(nlsys)])
+    @test nameof(nlsys) == nameof(sys)
+    @test !ModelingToolkit.iscomplete(nlsys)
+
+    sys1 = complete(sys; split = false)
+    nlsys = NonlinearSystem(sys1)
+    @test ModelingToolkit.iscomplete(nlsys)
+    @test !ModelingToolkit.is_split(nlsys)
+
+    sys2 = complete(sys)
+    nlsys = NonlinearSystem(sys2)
+    @test ModelingToolkit.iscomplete(nlsys)
+    @test ModelingToolkit.is_split(nlsys)
+
+    sys3 = structural_simplify(sys)
+    nlsys = NonlinearSystem(sys3)
+    @test length(equations(nlsys)) == length(ModelingToolkit.observed(nlsys)) == 1
+
+    prob = NonlinearProblem(sys3, [q => 2.0])
+    @test prob.f.initialization_data.initializeprobmap === nothing
+    sol = solve(prob)
+    @test SciMLBase.successful_retcode(sol)
+    @test sol.ps[p^3 + q^3]≈sol.ps[4r] atol=1e-10
+
+    @testset "Differential inside expression also substituted" begin
+        @named sys = ODESystem([0 ~ y * D(x) + x^2 - p, 0 ~ x * D(y) + y * p], t)
+        nlsys = NonlinearSystem(sys)
+        vs = ModelingToolkit.vars(equations(nlsys))
+        @test !in(D(x), vs)
+        @test !in(D(y), vs)
+    end
+end