New parameter type validation broke parameter splines

[hersle]

I need to integrate ODEs with splined input functions, which I pass as parameters. With version 9.15.0, this code works:

using Test
using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
using DifferentialEquations
using DataInterpolations: CubicSpline

@variables F(t)
@parameters Fspline
@register_symbolic Ffunc(t, spline)

ts = 0.0 : 0.01 : 1.0
Fs = ts .^ 2
Ffunc(t, spl) = spl(t) # evaluate spline

# evaluate splined F(t) through an ODESystem
@mtkbuild sys = ODESystem([F ~ Ffunc(t, Fspline)], t, [F], [Fspline])
prob = ODEProblem(sys, [], (0.0, 1.0), [Fspline => NaN]) # uninitialized problem
prob = remake(prob; p = [Fspline => CubicSpline(Fs, ts)])
sol = solve(prob)
@test sol(0.5, idxs=F) ≈ 0.5^2

But after the parameter type validation added in ea4d2fc and/or 6ae4b33, it fails with

ERROR: LoadError: TypeError: in validate_parameter_type, in Parameter Fspline, expected Real, got a value of type CubicSpline{Vector{Float64}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}, Vector{Float64}, Vector{Float64}, Float64}
Stacktrace:
 [1] validate_parameter_type(ic::ModelingToolkit.IndexCache, p::Num, index::ModelingToolkit.ParameterIndex{…}, val::CubicSpline{…})
   @ ModelingToolkit C:\Users\herma\.julia\packages\ModelingToolkit\wkMEe\src\systems\parameter_buffer.jl:459
 [2] remake_buffer(indp::ODEProblem{…}, oldbuf::ModelingToolkit.MTKParameters{…}, vals::Dict{…})
   @ ModelingToolkit C:\Users\herma\.julia\packages\ModelingToolkit\wkMEe\src\systems\parameter_buffer.jl:487
 [3] _updated_u0_p_symmap(prob::ODEProblem{…}, u0::Nothing, ::Val{…}, p::Dict{…}, ::Val{…})
   @ SciMLBase C:\Users\herma\.julia\packages\SciMLBase\JUp1I\src\remake.jl:486
 [4] _updated_u0_p_internal(prob::ODEProblem{…}, ::Missing, p::Vector{…}; interpret_symbolicmap::Bool, use_defaults::Bool)
   @ SciMLBase C:\Users\herma\.julia\packages\SciMLBase\JUp1I\src\remake.jl:399
 [5] _updated_u0_p_internal
   @ C:\Users\herma\.julia\packages\SciMLBase\JUp1I\src\remake.jl:388 [inlined]
 [6] #updated_u0_p#688
   @ C:\Users\herma\.julia\packages\SciMLBase\JUp1I\src\remake.jl:548 [inlined]
 [7] updated_u0_p
   @ C:\Users\herma\.julia\packages\SciMLBase\JUp1I\src\remake.jl:529 [inlined]
 [8] remake(prob::ODEProblem{…}; f::Missing, u0::Missing, tspan::Missing, p::Vector{…}, kwargs::Missing, interpret_symbolicmap::Bool, use_defaults::Bool, _kwargs::@Kwargs{})
   @ SciMLBase C:\Users\herma\.julia\packages\SciMLBase\JUp1I\src\remake.jl:95

I have tried to

• declare @parameters Fspline :: CubicSpline or @parameters Fspline(..) :: CubicSpline,
• pass Fspline => CubicSpline(Fs, ts) to ODEProblem instead of remake,
• evaluate Fspline(t) directly in the ODESystem equation, instead of through Ffunc(t, Fspline),

and mixes thereof, but I cannot seem to get it to work again. Maybe I am not doing it as I should.

Is it possible to make this work with the recent additions?

[AayushSabharwal]

Before DataInterpolations@5:

@variables F(t)
@parameters Fspline::Any
@register_symbolic Ffunc(t, spline::Any)

ts = 0.0 : 0.01 : 1.0
Fs = ts .^ 2
Ffunc(t, spl) = spl(t) # evaluate spline
@mtkbuild sys = ODESystem([F ~ Ffunc(t, Fspline)], t, [F], [Fspline])
prob = ODEProblem(sys, [], (0.0, 1.0), [Fspline => NaN]) # this only valid because of `::Any`. It's really not recommended
# ...

After DataInterpolations@5:

@variables F(t)
@parameters Fspline::CubicSpline
@register_symbolic Ffunc(t, spline::CubicSpline)

ts = 0.0 : 0.01 : 1.0
Fs = ts .^ 2
Ffunc(t, spl) = spl(t) # evaluate spline
@mtkbuild sys = ODESystem([F ~ Ffunc(t, Fspline)], t, [F], [Fspline])
# prob = ODEProblem(sys, [], (0.0, 1.0), [Fspline => NaN]) # this will error due to type validation
prob = ODEProblem(sys, [], (0.0, 1.0), [Fspline => CubicSpline(Fs, ts)])
# ...

Pre-v5, AbstractInterpolation subtyped AbstractArray which interferes with a lot of dispatches. Symbolics tries to wrap it in an Arr but fails because the eltype is Any, registration is similarly problematic, MTKParameters tries to convert it to a Vector, etc. To avoid all of this, the parameter is typed as Any.

After v5, this is no longer a problem. As long as the parameter and the registration are appropriately typed, everything works because the spline is correctly inferred as being nonnumeric. You can expand or restrict the type as required, as long as the value assigned to the parameter agrees with it.

[hersle]

Wonderful! This is exactly as I expect it to work, and much better than my previous hack.