feat: support callable parameters

Project.toml

@@ -24,6 +24,7 @@ ExprTools = "e2ba6199-217a-4e67-a87a-7c52f15ade04"
 Expronicon = "6b7a57c9-7cc1-4fdf-b7f5-e857abae3636"
 FindFirstFunctions = "64ca27bc-2ba2-4a57-88aa-44e436879224"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+FunctionWrappers = "069b7b12-0de2-55c6-9aab-29f3d0a68a2e"
 FunctionWrappersWrappers = "77dc65aa-8811-40c2-897b-53d922fa7daf"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
@@ -76,6 +77,7 @@ ChainRulesCore = "1"
 Combinatorics = "1"
 Compat = "3.42, 4"
 ConstructionBase = "1"
+DataInterpolations = "6.4"
 DataStructures = "0.17, 0.18"
 DeepDiffs = "1"
 DiffEqBase = "6.103.0"
@@ -91,6 +93,7 @@ ExprTools = "0.1.10"
 Expronicon = "0.8"
 FindFirstFunctions = "1"
 ForwardDiff = "0.10.3"
+FunctionWrappers = "1.1"
 FunctionWrappersWrappers = "0.1"
 Graphs = "1.5.2"
 InteractiveUtils = "1"
@@ -118,8 +121,8 @@ SparseArrays = "1"
 SpecialFunctions = "0.7, 0.8, 0.9, 0.10, 1.0, 2"
 StaticArrays = "0.10, 0.11, 0.12, 1.0"
 SymbolicIndexingInterface = "0.3.29"
-SymbolicUtils = "3.2"
-Symbolics = "6.3"
+SymbolicUtils = "3.7"
+Symbolics = "6.12"
 URIs = "1"
 UnPack = "0.1, 1.0"
 Unitful = "1.1"
@@ -129,6 +132,7 @@ julia = "1.9"
 AmplNLWriter = "7c4d4715-977e-5154-bfe0-e096adeac482"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 ControlSystemsBase = "aaaaaaaa-a6ca-5380-bf3e-84a91bcd477e"
+DataInterpolations = "82cc6244-b520-54b8-b5a6-8a565e85f1d0"
 DeepDiffs = "ab62b9b5-e342-54a8-a765-a90f495de1a6"
 DelayDiffEq = "bcd4f6db-9728-5f36-b5f7-82caef46ccdb"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
@@ -154,4 +158,4 @@ Sundials = "c3572dad-4567-51f8-b174-8c6c989267f4"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["AmplNLWriter", "BenchmarkTools", "ControlSystemsBase", "DelayDiffEq", "NonlinearSolve", "ForwardDiff", "Ipopt", "Ipopt_jll", "ModelingToolkitStandardLibrary", "Optimization", "OptimizationOptimJL", "OptimizationMOI", "OrdinaryDiffEq", "Random", "ReferenceTests", "SafeTestsets", "StableRNGs", "Statistics", "SteadyStateDiffEq", "Test", "StochasticDiffEq", "Sundials", "StochasticDelayDiffEq", "Pkg", "JET"]
+test = ["AmplNLWriter", "BenchmarkTools", "ControlSystemsBase", "DataInterpolations", "DelayDiffEq", "NonlinearSolve", "ForwardDiff", "Ipopt", "Ipopt_jll", "ModelingToolkitStandardLibrary", "Optimization", "OptimizationOptimJL", "OptimizationMOI", "OrdinaryDiffEq", "Random", "ReferenceTests", "SafeTestsets", "StableRNGs", "Statistics", "SteadyStateDiffEq", "Test", "StochasticDiffEq", "Sundials", "StochasticDelayDiffEq", "Pkg", "JET"]

src/ModelingToolkit.jl

@@ -38,6 +38,7 @@ using Base: RefValue
 using Combinatorics
 import Distributions
 import FunctionWrappersWrappers
+import FunctionWrappers: FunctionWrapper
 using URIs: URI
 using SciMLStructures
 using Compat
@@ -63,7 +64,8 @@ using Symbolics: _parse_vars, value, @derivatives, get_variables,
                  VariableSource, getname, variable, Connection, connect,
                  NAMESPACE_SEPARATOR, set_scalar_metadata, setdefaultval,
                  initial_state, transition, activeState, entry, hasnode,
-                 ticksInState, timeInState, fixpoint_sub, fast_substitute
+                 ticksInState, timeInState, fixpoint_sub, fast_substitute,
+                 CallWithMetadata, CallWithParent
 const NAMESPACE_SEPARATOR_SYMBOL = Symbol(NAMESPACE_SEPARATOR)
 import Symbolics: rename, get_variables!, _solve, hessian_sparsity,
                   jacobian_sparsity, isaffine, islinear, _iszero, _isone,

src/parameters.jl

@@ -26,6 +26,16 @@ function isparameter(x)
     end
 end
 
+function iscalledparameter(x)
+    x = unwrap(x)
+    return isparameter(getmetadata(x, CallWithParent, nothing))
+end
+
+function getcalledparameter(x)
+    x = unwrap(x)
+    return getmetadata(x, CallWithParent)
+end
+
 """
     toparam(s)
 

src/systems/index_cache.jl

@@ -32,6 +32,8 @@ struct DiscreteIndex
 end
 
 const ParamIndexMap = Dict{BasicSymbolic, Tuple{Int, Int}}
+const NonnumericMap = Dict{
+    Union{BasicSymbolic, Symbolics.CallWithMetadata}, Tuple{Int, Int}}
 const UnknownIndexMap = Dict{
     BasicSymbolic, Union{Int, UnitRange{Int}, AbstractArray{Int}}}
 const TunableIndexMap = Dict{BasicSymbolic,
@@ -45,20 +47,20 @@ struct IndexCache
     callback_to_clocks::Dict{Any, Vector{Int}}
     tunable_idx::TunableIndexMap
     constant_idx::ParamIndexMap
-    nonnumeric_idx::ParamIndexMap
+    nonnumeric_idx::NonnumericMap
     observed_syms::Set{BasicSymbolic}
     dependent_pars::Set{BasicSymbolic}
     discrete_buffer_sizes::Vector{Vector{BufferTemplate}}
     tunable_buffer_size::BufferTemplate
     constant_buffer_sizes::Vector{BufferTemplate}
     nonnumeric_buffer_sizes::Vector{BufferTemplate}
-    symbol_to_variable::Dict{Symbol, BasicSymbolic}
+    symbol_to_variable::Dict{Symbol, Union{BasicSymbolic, CallWithMetadata}}
 end
 
 function IndexCache(sys::AbstractSystem)
     unks = solved_unknowns(sys)
     unk_idxs = UnknownIndexMap()
-    symbol_to_variable = Dict{Symbol, BasicSymbolic}()
+    symbol_to_variable = Dict{Symbol, Union{BasicSymbolic, CallWithMetadata}}()
 
     let idx = 1
         for sym in unks
@@ -105,12 +107,11 @@ function IndexCache(sys::AbstractSystem)
 
     tunable_buffers = Dict{Any, Set{BasicSymbolic}}()
     constant_buffers = Dict{Any, Set{BasicSymbolic}}()
-    nonnumeric_buffers = Dict{Any, Set{BasicSymbolic}}()
+    nonnumeric_buffers = Dict{Any, Set{Union{BasicSymbolic, CallWithMetadata}}}()
 
-    function insert_by_type!(buffers::Dict{Any, Set{BasicSymbolic}}, sym)
+    function insert_by_type!(buffers::Dict{Any, S}, sym, ctype) where {S}
         sym = unwrap(sym)
-        ctype = symtype(sym)
-        buf = get!(buffers, ctype, Set{BasicSymbolic}())
+        buf = get!(buffers, ctype, S())
         push!(buf, sym)
     end
 
@@ -142,7 +143,7 @@ function IndexCache(sys::AbstractSystem)
                 clocks = get!(() -> Set{Int}(), disc_param_callbacks, sym)
                 push!(clocks, i)
             else
-                insert_by_type!(constant_buffers, sym)
+                insert_by_type!(constant_buffers, sym, symtype(sym))
             end
         end
     end
@@ -197,6 +198,9 @@ function IndexCache(sys::AbstractSystem)
     for p in parameters(sys)
         p = unwrap(p)
         ctype = symtype(p)
+        if ctype <: FnType
+            ctype = fntype_to_function_type(ctype)
+        end
         haskey(disc_idxs, p) && continue
         haskey(constant_buffers, ctype) && p in constant_buffers[ctype] && continue
         insert_by_type!(
@@ -212,12 +216,13 @@ function IndexCache(sys::AbstractSystem)
             else
                 nonnumeric_buffers
             end,
-            p
+            p,
+            ctype
         )
     end
 
-    function get_buffer_sizes_and_idxs(buffers::Dict{Any, Set{BasicSymbolic}})
-        idxs = ParamIndexMap()
+    function get_buffer_sizes_and_idxs(T, buffers::Dict)
+        idxs = T()
         buffer_sizes = BufferTemplate[]
         for (i, (T, buf)) in enumerate(buffers)
             for (j, p) in enumerate(buf)
@@ -229,13 +234,18 @@ function IndexCache(sys::AbstractSystem)
                 idxs[rp] = (i, j)
                 idxs[rttp] = (i, j)
             end
+            if T <: Symbolics.FnType
+                T = Any
+            end
             push!(buffer_sizes, BufferTemplate(T, length(buf)))
         end
         return idxs, buffer_sizes
     end
 
-    const_idxs, const_buffer_sizes = get_buffer_sizes_and_idxs(constant_buffers)
-    nonnumeric_idxs, nonnumeric_buffer_sizes = get_buffer_sizes_and_idxs(nonnumeric_buffers)
+    const_idxs, const_buffer_sizes = get_buffer_sizes_and_idxs(
+        ParamIndexMap, constant_buffers)
+    nonnumeric_idxs, nonnumeric_buffer_sizes = get_buffer_sizes_and_idxs(
+        NonnumericMap, nonnumeric_buffers)
 
     tunable_idxs = TunableIndexMap()
     tunable_buffer_size = 0
@@ -401,7 +411,8 @@ function reorder_parameters(ic::IndexCache, ps; drop_missing = false)
     for temp in ic.discrete_buffer_sizes)
     const_buf = Tuple(BasicSymbolic[unwrap(variable(:DEF)) for _ in 1:(temp.length)]
     for temp in ic.constant_buffer_sizes)
-    nonnumeric_buf = Tuple(BasicSymbolic[unwrap(variable(:DEF)) for _ in 1:(temp.length)]
+    nonnumeric_buf = Tuple(Union{BasicSymbolic, CallWithMetadata}[unwrap(variable(:DEF))
+                                                                  for _ in 1:(temp.length)]
     for temp in ic.nonnumeric_buffer_sizes)
     for p in ps
         p = unwrap(p)
@@ -481,3 +492,7 @@ function get_buffer_template(ic::IndexCache, pidx::ParameterIndex)
         error("Unhandled portion $portion")
     end
 end
+
+fntype_to_function_type(::Type{FnType{A, R, T}}) where {A, R, T} = T
+fntype_to_function_type(::Type{FnType{A, R, Nothing}}) where {A, R} = FunctionWrapper{R, A}
+fntype_to_function_type(::Type{FnType{A, R}}) where {A, R} = FunctionWrapper{R, A}

src/systems/parameter_buffer.jl

@@ -152,6 +152,9 @@ function MTKParameters(
         if symbolic_type(val) !== NotSymbolic()
             error("Could not evaluate value of parameter $sym. Missing values for variables in expression $val.")
         end
+        if ctype <: FnType
+            ctype = fntype_to_function_type(ctype)
+        end
         val = symconvert(ctype, val)
         done = set_value(sym, val)
         if !done && Symbolics.isarraysymbolic(sym)

src/systems/systemstructure.jl

@@ -661,7 +661,8 @@ function structural_simplify!(state::TearingState, io = nothing; simplify = fals
             @set! sys.defaults = merge(ModelingToolkit.defaults(sys),
                 Dict(v => 0.0 for v in Iterators.flatten(inputs)))
         end
-        ps = [setmetadata(sym, VariableTimeDomain, get(time_domains, sym, Continuous))
+        ps = [sym isa CallWithMetadata ? sym :
+              setmetadata(sym, VariableTimeDomain, get(time_domains, sym, Continuous))
               for sym in get_ps(sys)]
         @set! sys.ps = ps
     else

src/utils.jl

@@ -371,7 +371,11 @@ end
 vars(exprs::Num; op = Differential) = vars(unwrap(exprs); op)
 vars(exprs::Symbolics.Arr; op = Differential) = vars(unwrap(exprs); op)
 function vars(exprs; op = Differential)
-    foldl((x, y) -> vars!(x, unwrap(y); op = op), exprs; init = Set())
+    if hasmethod(iterate, Tuple{typeof(exprs)})
+        foldl((x, y) -> vars!(x, unwrap(y); op = op), exprs; init = Set())
+    else
+        vars!(Set(), unwrap(exprs); op)
+    end
 end
 vars(eq::Equation; op = Differential) = vars!(Set(), eq; op = op)
 function vars!(vars, eq::Equation; op = Differential)
@@ -479,7 +483,11 @@ end
 
 function collect_var!(unknowns, parameters, var, iv)
     isequal(var, iv) && return nothing
-    if isparameter(var) || (iscall(var) && isparameter(operation(var)))
+    if iscalledparameter(var)
+        callable = getcalledparameter(var)
+        push!(parameters, callable)
+        collect_vars!(unknowns, parameters, arguments(var), iv)
+    elseif isparameter(var) || (iscall(var) && isparameter(operation(var)))
         push!(parameters, var)
     elseif !isconstant(var)
         push!(unknowns, var)

test/odesystem.jl

@@ -137,15 +137,15 @@ eqs = [D(x) ~ σ(t - 1) * (y - x),
     D(y) ~ x * (ρ - z) - y,
     D(z) ~ x * y - β * z * κ]
 @named de = ODESystem(eqs, t)
-test_diffeq_inference("single internal iv-varying", de, t, (x, y, z), (σ(t - 1), ρ, β))
+test_diffeq_inference("single internal iv-varying", de, t, (x, y, z), (σ, ρ, β))
 f = eval(generate_function(de, [x, y, z], [σ, ρ, β])[2])
 du = [0.0, 0.0, 0.0]
 f(du, [1.0, 2.0, 3.0], [x -> x + 7, 2, 3], 5.0)
 @test du ≈ [11, -3, -7]
 
 eqs = [D(x) ~ x + 10σ(t - 1) + 100σ(t - 2) + 1000σ(t^2)]
 @named de = ODESystem(eqs, t)
-test_diffeq_inference("many internal iv-varying", de, t, (x,), (σ(t - 2), σ(t^2), σ(t - 1)))
+test_diffeq_inference("many internal iv-varying", de, t, (x,), (σ,))
 f = eval(generate_function(de, [x], [σ])[2])
 du = [0.0]
 f(du, [1.0], [t -> t + 2], 5.0)

test/split_parameters.jl

@@ -1,11 +1,13 @@
 using ModelingToolkit, Test
 using ModelingToolkitStandardLibrary.Blocks
 using OrdinaryDiffEq
+using DataInterpolations
 using BlockArrays: BlockedArray
 using ModelingToolkit: t_nounits as t, D_nounits as D
 using ModelingToolkit: MTKParameters, ParameterIndex, NONNUMERIC_PORTION
 using SciMLStructures: Tunable, Discrete, Constants
 using StaticArrays: SizedVector
+using SymbolicIndexingInterface: is_parameter, getp
 
 x = [1, 2.0, false, [1, 2, 3], Parameter(1.0)]
 
@@ -219,3 +221,46 @@ S = get_sensitivity(closed_loop, :u)
     @test ps[ParameterIndex(Tunable(), 1:8)] == collect(1.0:8.0) .+ 0.5
     @test ps[ParameterIndex(Discrete(), (2, 1, 2, 2))] == 5
 end
+
+@testset "Callable parameters" begin
+    @testset "As FunctionWrapper" begin
+        _f1(x) = 2x
+        struct Foo end
+        (::Foo)(x) = 3x
+        @variables x(t)
+        @parameters fn(::Real) = _f1
+        @mtkbuild sys = ODESystem(D(x) ~ fn(t), t)
+        @test is_parameter(sys, fn)
+        @test ModelingToolkit.defaults(sys)[fn] == _f1
+
+        getter = getp(sys, fn)
+        prob = ODEProblem(sys, [x => 1.0], (0.0, 1.0))
+        @inferred getter(prob)
+        # cannot be inferred better since `FunctionWrapper` is only known to return `Real`
+        @inferred Vector{<:Real} prob.f(prob.u0, prob.p, prob.tspan[1])
+        sol = solve(prob, Tsit5(); abstol = 1e-10, reltol = 1e-10)
+        @test sol.u[end][] ≈ 2.0
+
+        prob = ODEProblem(sys, [x => 1.0], (0.0, 1.0), [fn => Foo()])
+        @inferred getter(prob)
+        @inferred Vector{<:Real} prob.f(prob.u0, prob.p, prob.tspan[1])
+        sol = solve(prob; abstol = 1e-10, reltol = 1e-10)
+        @test sol.u[end][] ≈ 2.5
+    end
+
+    @testset "Concrete function type" begin
+        ts = 0.0:0.1:1.0
+        interp = LinearInterpolation(ts .^ 2, ts; extrapolate = true)
+        @variables x(t)
+        @parameters (fn::typeof(interp))(..)
+        @mtkbuild sys = ODESystem(D(x) ~ fn(x), t)
+        @test is_parameter(sys, fn)
+        getter = getp(sys, fn)
+        prob = ODEProblem(sys, [x => 1.0], (0.0, 1.0), [fn => interp])
+        @inferred getter(prob)
+        @inferred prob.f(prob.u0, prob.p, prob.tspan[1])
+        @test_nowarn sol = solve(prob, Tsit5())
+        @test_nowarn prob.ps[fn] = LinearInterpolation(ts .^ 3, ts; extrapolate = true)
+        @test_nowarn sol = solve(prob)
+    end
+end