feat: allow complex for NNODE

[sathvikbhagavan]

It works with all except QuadratureTraining.

First I get this error:

ERROR: ArgumentError: Cannot create a dual over scalar type ComplexF64. If the type behaves as a scalar, define ForwardDiff.can_dual(::Type{ComplexF64}) = true.

After setting ForwardDiff.can_dual(::Type{ComplexF64}) = true, I get:

ERROR: MethodError: no method matching typemax(::Type{ComplexF64})

Closest candidates are:
  typemax(::Type{Num})
   @ Symbolics ~/.julia/packages/Symbolics/VkJPk/src/num.jl:33
  typemax(::Type{Base.TCSETATTR_FLAGS})
   @ Base Enums.jl:216
  typemax(::Type{ModelingToolkit.BipartiteGraphs.VertType})
   @ ModelingToolkit Enums.jl:216
  ...

Stacktrace:
  [1] (::Cubature.var"#17#18"{Bool, Bool, Int64, Float64, Float64, Int64, Int32, Ptr{…}, Cubature.IntegrandData{…}, Vector{…}, Vector{…}, Vector{…}, Vector{…}, Int64})()
    @ Cubature ~/.julia/packages/Cubature/5zwuu/src/Cubature.jl:215
  [2] disable_sigint
    @ ./c.jl:473 [inlined]
  [3] cubature(xscalar::Bool, fscalar::Bool, vectorized::Bool, padaptive::Bool, fdim::Int64, f::IntegralsCubatureExt.var"#3#10"{…}, xmin_::Float64, xmax_::Float64, reqRelError::Float64, reqAbsError::Float64, maxEval::Int64, error_norm::Int32)
    @ Cubature ~/.julia/packages/Cubature/5zwuu/src/Cubature.jl:169
  [4] hquadrature_v
    @ ~/.julia/packages/Cubature/5zwuu/src/Cubature.jl:230 [inlined]
  [5] #__solvebp_call#1
    @ ~/.julia/packages/Integrals/tvunm/ext/IntegralsCubatureExt.jl:43 [inlined]
  [6] __solvebp_call
    @ ~/.julia/packages/Integrals/tvunm/ext/IntegralsCubatureExt.jl:7 [inlined]
  [7] #__solvebp_call#4
    @ ~/.julia/packages/Integrals/tvunm/src/common.jl:115 [inlined]
  [8] __solvebp_call
    @ ~/.julia/packages/Integrals/tvunm/src/common.jl:114 [inlined]
  [9] __solvebp(cache::Integrals.IntegralCache{…}, alg::Integrals.CubatureJLh, sensealg::Integrals.ReCallVJP{…}, domain::Tuple{…}, p::ComponentArrays.ComponentVector{…}; kwargs::@Kwargs{…})
    @ IntegralsForwardDiffExt ~/.julia/packages/Integrals/tvunm/ext/IntegralsForwardDiffExt.jl:99
 [10] solve!(cache::Integrals.IntegralCache{…})
    @ Integrals ~/.julia/packages/Integrals/tvunm/src/common.jl:105
 [11] solve(prob::IntegralProblem{…}, alg::Integrals.CubatureJLh; kwargs::@Kwargs{…})
    @ Integrals ~/.julia/packages/Integrals/tvunm/src/common.jl:101
 [12] (::NeuralPDE.var"#loss#188"{…})(θ::ComponentArrays.ComponentVector{…}, ::NeuralPDE.ODEPhi{…})
    @ NeuralPDE ~/NeuralPDE.jl/src/ode_solve.jl:231
 [13] total_loss
    @ ~/NeuralPDE.jl/src/ode_solve.jl:400 [inlined]
 [14] (::OptimizationForwardDiffExt.var"#37#55"{…})(::ComponentArrays.ComponentVector{…})
    @ OptimizationForwardDiffExt ~/.julia/packages/OptimizationBase/rRpJs/ext/OptimizationForwardDiffExt.jl:98
 [15] #39
    @ ~/.julia/packages/OptimizationBase/rRpJs/ext/OptimizationForwardDiffExt.jl:102 [inlined]
 [16] chunk_mode_gradient!(result::ComponentArrays.ComponentVector{…}, f::OptimizationForwardDiffExt.var"#39#57"{…}, x::ComponentArrays.ComponentVector{…}, cfg::ForwardDiff.GradientConfig{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/gradient.jl:123
 [17] gradient!
    @ ~/.julia/packages/ForwardDiff/PcZ48/src/gradient.jl:39 [inlined]
 [18] (::OptimizationForwardDiffExt.var"#38#56"{…})(::ComponentArrays.ComponentVector{…}, ::ComponentArrays.ComponentVector{…})
    @ OptimizationForwardDiffExt ~/.julia/packages/OptimizationBase/rRpJs/ext/OptimizationForwardDiffExt.jl:102
 [19] macro expansion
    @ ~/.julia/packages/OptimizationOptimisers/AOkbT/src/OptimizationOptimisers.jl:68 [inlined]
 [20] macro expansion
    @ ~/.julia/packages/Optimization/5DEdF/src/utils.jl:32 [inlined]
 [21] __solve(cache::OptimizationBase.OptimizationCache{…})
    @ OptimizationOptimisers ~/.julia/packages/OptimizationOptimisers/AOkbT/src/OptimizationOptimisers.jl:66
 [22] solve!(cache::OptimizationBase.OptimizationCache{…})
    @ SciMLBase ~/.julia/packages/SciMLBase/NjslX/src/solve.jl:180
 [23] solve(::OptimizationProblem{…}, ::Optimisers.Adam; kwargs::@Kwargs{…})
    @ SciMLBase ~/.julia/packages/SciMLBase/NjslX/src/solve.jl:96
 [24] __solve(::ODEProblem{…}, ::NNODE{…}; dt::Nothing, timeseries_errors::Bool, save_everystep::Bool, adaptive::Bool, abstol::Float32, reltol::Float32, verbose::Bool, saveat::Float64, maxiters::Int64, tstops::Nothing)
    @ NeuralPDE ~/NeuralPDE.jl/src/ode_solve.jl:440
 [25] solve_call(_prob::ODEProblem{…}, args::NNODE{…}; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/8vI1R/src/solve.jl:612
 [26] solve_up(prob::ODEProblem{…}, sensealg::Nothing, u0::Vector{…}, p::Vector{…}, args::NNODE{…}; kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/8vI1R/src/solve.jl:1080
 [27] solve(prob::ODEProblem{…}, args::NNODE{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/8vI1R/src/solve.jl:1003
 [28] top-level scope
    @ REPL[22]:1
Some type information was truncated. Use `show(err)` to see complete types.

I am not sure how to fix this.

[ChrisRackauckas]

For now, make it throw a good high level error and get it merged. Document the caveat. I think solving that is a much bigger detail.