Trying to use data as an initial condition for a 1D diffusion problem with DiffEqOperators.jl

Using code from Example 1 in the library repo README to get started.

I’m getting ERROR: MethodError: no method matching zero(::Type{Vector{Float64}}) and not clear how to decode the Stacktrace …

using OrdinaryDiffEq, ModelingToolkit, DiffEqOperators, DomainSets, DifferentialEquations, Interpolations
###
function uniform_linear_sample(data_in, n_samples)
        # Resample a 1D dataset using a given number of sample points using linear interpolation.
    
        nodes_in = range(1, size(data_in)[1], length=length(data_in))
        nodes_eval = range(1, Int(nodes_in[end]), length = Int(n_samples))
    
        int = interpolate((nodes_in,), data_in, Gridded(Linear()))
    
        data_out = zeros(length(nodes_eval))
        idx = trues(length(nodes_eval))
    
        data_out[idx] = int(nodes_eval[idx])
    
        return data_out
end

n_nodes = 1000

x_ic = range(0,Float64(2pi),length=10000)
data_vector = cos.(x_ic) .+ 1

ic() = uniform_linear_sample(data_vector,n_nodes)

@register ic()
###
# Parameters, variables, and derivatives
@parameters t x
@variables u(..)
Dt = Differential(t)
Dxx = Differential(x)^2

# 1D PDE and boundary conditions
eq  = Dt(u(t,x)) ~ Dxx(u(t,x))
bcs = [u(0,x) ~ ic(),
       u(t,0) ~ exp(-t),
       u(t,Float64(pi)) ~ -exp(-t)]

# Space and time domains
domains = [t ∈ Interval(0.0,1.0),
           x ∈ Interval(0.0,Float64(2pi))]

# PDE system
@named pdesys = PDESystem(eq,bcs,domains,[t,x],[u(t,x)])

# Method of lines discretization
dx = 0.1
order = 2
discretization = MOLFiniteDifference([x=>dx],t;centered_order=order)

# Convert the PDE problem into an ODE problem
prob = discretize(pdesys,discretization)

# Solve ODE problem
sol = solve(prob,saveat=0.1)
ERROR: LoadError: MethodError: no method matching zero(::Type{Vector{Float64}})
Closest candidates are:
  zero(::Union{Type{P}, P}) where P<:Dates.Period at C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\Dates\src\periods.jl:53
  zero(::ExtendedJumpArray) at C:\Users\thompsmj.X-MJIS3050PC09\.julia\packages\DiffEqJump\x05Qi\src\extended_jump_array.jl:26
  zero(::Unitful.AbstractQuantity{T, D, U} where {T, D, U<:(Unitful.Units{N, D, A} where {N, D, A<:Unitful.Affine})}) at C:\Users\thompsmj.X-MJIS3050PC09\.julia\packages\Unitful\yI5QN\src\quantities.jl:374
  ...
Stacktrace:
 [1] zero(x::Vector{Vector{Float64}})
   @ Base .\abstractarray.jl:1085

make it ic(x) and use a callable.

Hi Chris, thanks for trying to help, but I’m still unclear. I can interpolate the data fine, but I don’t understand what to do to “use a callable,” though I’ve been going through the docs to try to get the hang of it.

I tried using exactly what I have posted above, and swapping in this line as you suggest:

bcs = [u(0,x) ~ ic(x),
       u(t,0) ~ exp(-t),
       u(t,Float64(pi)) ~ -exp(-t)]

And I get

ERROR: LoadError: MethodError: no method matching ic(::Num)

on that line.

Above that, I then tried

ic(x) = uniform_linear_sample(data_vector,n_nodes)

which gets through to the end and gives this error at the solve line

sol = solve(prob,saveat=0.1)

ERROR: LoadError: MethodError: no method matching zero(::Type{Vector{Float64}})

Edit: fixed link to wrong place.

Why not just use the DataInterpolations.jl linear interpolation?

Didn’t know about it! Looks like a useful library.

Trying it out though I’m getting LoadError: UndefVarError: LinearInterpolation not defined with the current v3.6.1.

Show what you ran.

OK, the issue with LinearInterpolation not defined is resolved if I don’t load Interpolations and DataInterpolations together.

using DataInterpolations, Interpolations
u = rand(5)
t = 0:4
interp = LinearInterpolation(u,t)

ERROR: LoadError: UndefVarError: LinearInterpolation not defined
using DataInterpolations
u = rand(5)
t = 0:4
interp = LinearInterpolation(u,t)

10-element LinearInterpolation{Vector{Float64}, UnitRange{Int64}, true, Float64}:

This is where I’m unfamiliar with symbolic programming, so the final line gives LoadError: MethodError: no method matching munge_data(::Vector{Float64}, ::Float64)

running:

using OrdinaryDiffEq, ModelingToolkit, DiffEqOperators, DomainSets, DifferentialEquations, DataInterpolations

x_dense = range(0,Float64(2pi),length=10000)
data = cos.(x_dense) .+ 1.0 .+ 0.05*randn(10000)

# Parameters, variables, and derivatives
@parameters t x
@variables u(..)
Dt = Differential(t)
Dxx = Differential(x)^2

# 1D PDE and boundary conditions
ic(x) = LinearInterpolation(data, x)
@register ic(x)
eq  = Dt(u(t,x)) ~ Dxx(u(t,x))
bcs = [u(0,x) ~ ic(x),
       u(t,0) ~ exp(-t),
       u(t,Float64(pi)) ~ -exp(-t)]

# Space and time domains
domains = [t ∈ Interval(0.0,1.0),
           x ∈ Interval(0.0,Float64(2pi))]

# PDE system
@named pdesys = PDESystem(eq,bcs,domains,[t,x],[u(t,x)])

# Method of lines discretization
dx = 0.1
order = 2
discretization = MOLFiniteDifference([x=>dx],t;centered_order=order)

# Convert the PDE problem into an ODE problem
prob = discretize(pdesys,discretization)

Also tried ic(x) = LinearInterpolation(data, 0:Float64(2pi)) with all else the same, and running prob = discretize(pdesys,discretization) succeeds, giving:

ODEProblem with uType Vector{LinearInterpolation{Vector{Float64}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}}, true, Float64}} and tType Float64. In-place: true

but sol = solve(prob,Tsit5(),saveat=0.1) gives:

ERROR: LoadError: MethodError: Cannot `convert` an object of type Vector{Float64} to an object of type LinearInterpolation{Vector{Float64}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}}, true, Float64}

No, LinearInterpolation is a callable. Look at the documentation.

using DataInterpolations
u = rand(5)
t = 0:4
interp = LinearInterpolation(u,t)
interp(t)

Because of that, you do:

ic = LinearInterpolation(data, x_dense)

now ic(x) is the interpolation function over the data, which means

@register ic(x)
bcs = [u(0,x) ~ ic(x),
       u(t,0) ~ exp(-t),
       u(t,Float64(pi)) ~ -exp(-t)]

will work.

using OrdinaryDiffEq, ModelingToolkit, DiffEqOperators, DomainSets, DifferentialEquations, DataInterpolations

x_dense = range(0,Float64(2pi),length=10000)
data = cos.(x_dense) .+ 1.0 

# Parameters, variables, and derivatives
@parameters t x
@variables u(..)
Dt = Differential(t)
Dxx = Differential(x)^2

# 1D PDE and boundary conditions
ic = LinearInterpolation(data, x_dense)
@register ic(x)
ERROR: LoadError: cannot define function ic; it already has a value

ic iteself is:

julia> ic
20000-element LinearInterpolation{Vector{Float64}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}}, true, Float64}:

ic(x) is:

julia> ic(x)
ERROR: MethodError: isless(::Num, ::Float64) is ambiguous. Candidates:
  isless(x::Real, y::AbstractFloat) in Base at operators.jl:168
  isless(a::Num, b::Real) in Symbolics at C:\Users\thompsmj.X-MJIS3050PC09\.julia\packages\Symbolics\Cmx10\src\num.jl:130
Possible fix, define
  isless(::Num, ::AbstractFloat)

The answer is in Register Interpolations for Symbolics by ChrisRackauckas · Pull Request #93 · PumasAI/DataInterpolations.jl · GitHub .

import Symbolics
(interp::DataInterpolations.AbstractInterpolation)(t::Symbolics.Num) = Symbolics.SymbolicUtils.term(interp,t)

and the release with that will make it automatic.

I’ve been running into similar issues using DataInterpolations’s CubicSplines in ModelingToolkit. The pull request provided by @ChrisRackauckas looks like it may fix my problems, but I can’t update Symbolics to the latest version. There’s some sort of incompatibility with the packages in ModelingToolkit. Any thoughts?

pkg> add Symbolics@4.0
   Resolving package versions...
ERROR: Unsatisfiable requirements detected for package ModelingToolkit [961ee093]:
 ModelingToolkit [961ee093] log:
 ├─possible versions are: 0.0.1-6.7.1 or uninstalled
 ├─restricted to versions * by QED [03dc1bc1], leaving only versions 0.0.1-6.7.1
 │ └─QED [03dc1bc1] log:
 │   ├─possible versions are: 0.1.0 or uninstalled
 │   └─QED [03dc1bc1] is fixed to version 0.1.0
 ├─restricted by compatibility requirements with Symbolics [0c5d862f] to versions: 0.0.1-5.9.1 or uninstalled, leaving only versions: 0.0.1-5.9.1
 │ └─Symbolics [0c5d862f] log:
 │   ├─possible versions are: 0.1.0-4.0.0 or uninstalled
 │   ├─restricted to versions * by QED [03dc1bc1], leaving only versions 0.1.0-4.0.0
 │   │ └─QED [03dc1bc1] log: see above
 │   └─restricted to versions 4.0 by an explicit requirement, leaving only versions 4.0.0
 ├─restricted by compatibility requirements with RuntimeGeneratedFunctions [7e49a35a] to versions: [0.0.1-3.21.0, 4.5.0-6.7.1] or uninstalled, leaving only versions: [0.0.1-3.21.0, 4.5.0-5.9.1]
 │ └─RuntimeGeneratedFunctions [7e49a35a] log:
 │   ├─possible versions are: 0.1.0-0.5.3 or uninstalled
 │   └─restricted by compatibility requirements with Symbolics [0c5d862f] to versions: 0.5.0-0.5.3
 │     └─Symbolics [0c5d862f] log: see above
 ├─restricted by compatibility requirements with Latexify [23fbe1c1] to versions: [0.0.1-0.8.0, 1.2.7-6.7.1] or uninstalled, leaving only versions: [0.0.1-0.8.0, 1.2.7-3.21.0, 4.5.0-5.9.1]
 │ └─Latexify [23fbe1c1] log:
 │   ├─possible versions are: 0.5.0-0.15.9 or uninstalled
 │   ├─restricted by compatibility requirements with Symbolics [0c5d862f] to versions: 0.11.0-0.15.9
 │   │ └─Symbolics [0c5d862f] log: see above
 │   └─restricted by compatibility requirements with Requires [ae029012] to versions: 0.13.0-0.15.9 or uninstalled, leaving only versions: 0.13.0-0.15.9
 │     └─Requires [ae029012] log:
 │       ├─possible versions are: 0.5.0-1.1.3 or uninstalled
 │       └─restricted by compatibility requirements with Symbolics [0c5d862f] to versions: 1.1.0-1.1.3
 │         └─Symbolics [0c5d862f] log: see above
 ├─restricted by compatibility requirements with StaticArrays [90137ffa] to versions: 4.0.7-6.7.1 or uninstalled, leaving only versions: 4.5.0-5.9.1
 │ └─StaticArrays [90137ffa] log:
 │   ├─possible versions are: 0.8.0-1.2.13 or uninstalled
 │   ├─restricted to versions * by Equilibrium [187daef3], leaving only versions 0.8.0-1.2.13
 │   │ └─Equilibrium [187daef3] log:
 │   │   ├─possible versions are: 0.1.0 or uninstalled
 │   │   └─Equilibrium [187daef3] is fixed to version 0.1.0
 │   ├─restricted by compatibility requirements with ForwardDiff [f6369f11] to versions: 0.8.3-1.2.13
 │   │ └─ForwardDiff [f6369f11] log:
 │   │   ├─possible versions are: 0.9.0-0.10.21 or uninstalled
 │   │   ├─restricted to versions * by Equilibrium [187daef3], leaving only versions 0.9.0-0.10.21
 │   │   │ └─Equilibrium [187daef3] log: see above
 │   │   ├─restricted by compatibility requirements with DiffRules [b552c78f] to versions: 0.10.6-0.10.21 or uninstalled, leaving only versions: 0.10.6-0.10.21
 │   │   │ └─DiffRules [b552c78f] log:
 │   │   │   ├─possible versions are: 0.0.8-1.3.1 or uninstalled
 │   │   │   ├─restricted by compatibility requirements with ForwardDiff [f6369f11] to versions: [0.0.8-1.0.2, 1.2.1-1.3.1]
 │   │   │   │ └─ForwardDiff [f6369f11] log: see above
 │   │   │   └─restricted by compatibility requirements with Symbolics [0c5d862f] to versions: 0.1.0-1.3.1, leaving only versions: [0.1.0-1.0.2, 1.2.1-1.3.1]
 │   │   │     └─Symbolics [0c5d862f] log: see above
 │   │   └─restricted by compatibility requirements with StaticArrays [90137ffa] to versions: 0.10.13-0.10.21 or uninstalled, leaving only versions: 0.10.13-0.10.21
 │   │     └─StaticArrays [90137ffa] log: see above
 │   └─restricted by compatibility requirements with Symbolics [0c5d862f] to versions: 1.1.0-1.2.13
 │     └─Symbolics [0c5d862f] log: see above
 └─restricted by compatibility requirements with SymbolicUtils [d1185830] to versions: 0.0.1-3.1.1 or uninstalled — no versions left
   └─SymbolicUtils [d1185830] log:
     ├─possible versions are: 0.1.0-0.18.0 or uninstalled
     └─restricted by compatibility requirements with Symbolics [0c5d862f] to versions: 0.18.0
       └─Symbolics [0c5d862f] log: see above

Symbolics.jl v4 was just released, and this requires that update. So some downstream updates will need to be done before this can really be used everywhere. Working on it :sweat_smile:

1 Like

Sounds good, thanks!