Use of Interpolations with ModelingToolkit

Hi,

I’m using ModelingToolkit to model a battery cell using the Equivalent Circuit Model (ECM) approach. For that, I will be using 2-D lookup tables for the values of Vocv, resistnaces and time constants/capacitances, where the breakpoints are SoC and Temperature.

As I want to identify the model parameters, I want to set the lookup table data as parameters.

I’m now struggling with the interpolation function. I cannot make the Interpolations.LinearInterpolation from Interpolations.jl work. Below is a toy problem that presents the issue:

using ModelingToolkit, Interpolations, DifferentialEquations
using ModelingToolkit: t_nounits as t, D_nounits as D
using Plots;
plotlyjs();

function lut_1d(X1, Data, bp1)
    interpolator = Interpolations.LinearInterpolation((bp1), Data, extrapolation_bc=Flat())
    return interpolator(X1)
end
@register_symbolic lut_1d(X1,Data,bp1)

@parameters table_data[1:3] = [1.0, 2.0, 3.0]
@variables soc(t) R(t) i(t) V(t)
@constants table_bkp = [0.0, 0.5, 1.0]

eqs_interp = [ D(soc) ~ -i/3600/1
                R      ~ lut_1d(t, table_data, table_bkp)
                V      ~ R * i
                V      ~ 1
]

@named sys_interp = ODESystem(eqs_interp, t)
sys_interp = structural_simplify(sys_interp)

With that, I get the error:

MethodError: no method matching LinearInterpolation(::Num, ::Symbolics.Arr{Num, 1}; extrapolation_bc::Flat{Nothing})

Any suggestions on how to make this work?

Hello and welcome to the community :wave:

Try GitHub - SciML/DataInterpolations.jl: A library of data interpolation and smoothing functions instead, they are made to work with MTK.

If you don’t have to make the data parameters, I would avoid it and keep the data as normal numeric arrays.

See an example of using interpolations here

1 Like

Many thanks for the quick reply!

I have updated the script the the below, but it seems I’m missing something, probably related to the registration of the lut1 function.

using ModelingToolkit, DataInterpolations, DifferentialEquations
using ModelingToolkit: t_nounits as t, D_nounits as D
using Plots;
plotlyjs();

function lut1(x, data, bp_x)
    interpolator = DataInterpolations.LinearInterpolation(data, bp_x)
    if x > bp_x[end]
        return data[end]
    elseif x < bp_x[1]
        return data[1]
    else
        return interpolator(x)
    end
end

@register_symbolic lut_1d(x::Num, data::Symbolics.Arr{Num, 1}, bp_x::Num)

@parameters table_data[1:3] = [1.0, 2.0, 3.0]
@variables soc(t) R(t) i(t) V(t)
@constants table_bkp = [0.0, 0.5, 1.0]

eqs_interp = [ D(soc) ~ -i/3600/1
                R      ~ lut_1d(t, table_data, table_bkp)
                V      ~ R * i
                V      ~ 1
]

@named sys_interp = ODESystem(eqs_interp, t)
sys_interp = structural_simplify(sys_interp)

u0 = [soc => 0.5
      i   => 0.0]
prob_interp = ODEProblem(sys_interp, u0, (0.0, 10.0))
sol_interp = solve(prob_interp)
plot(sol_interp)

With that code above, I get this error:

MethodError: no method matching lut_1d(::Float64, ::SubArray{Float64, 1, Vector{Float64}, Tuple{UnitRange{Int64}}, true}, ::Vector{Float64})

There is now a tutorial to help you and anyone else trying similar things. Check out Callable parameters and interpolating data · ModelingToolkit.jl. If you still have questions, please ask and I can update the documentation to make it clearer.

1 Like

Hi! Many thaks for the pointer! The exmaple worked, but only when I use it outside @mtkmodel / @mtkbuild models.

I found this example, which uses MTK Standard Library, which has a Interpolation block:

but the example does not use it uses @mtkmodel / @mtkbuild .

When I try the following:

@mtkmodel model_with_lut begin

    @parameters begin
        table_data = [1.0, 2.0, 3.0]
        table_bkp = [0.0, 0.5, 1.0]
    end

    @components begin
        src = Interpolation(LinearInterpolation, table_data, table_bkp)
        clk = ContinuousClock()
        model = MassSpringDamper()
    end
    @equations begin
        connect(src.input, clk.output)
        connect(src.output, model.input)
    end
end;

@mtkbuild model_with_lut_model = model_with_lut()

I get

MethodError: no method matching Interpolation(; name::Symbol, LinearInterpolation::UnionAll, table_data::Num, table_bkp::Num)
The function `Interpolation` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  Interpolation(::Any; name) got unsupported keyword arguments "LinearInterpolation", "table_data", "table_bkp"
   @ ModelingToolkitStandardLibrary ~/.julia/packages/ModelingToolkitStandardLibrary/RaBbh/src/Blocks/sources.jl:765
  Interpolation(::Any, ::Any, ::Any, ::Any...; name) got unsupported keyword arguments "LinearInterpolation", "table_data", "table_bkp"
   @ ModelingToolkitStandardLibrary ~/.julia/packages/ModelingToolkitStandardLibrary/RaBbh/src/Blocks/sources.jl:760

Wha tam I missing?

It’s brand new, like last week. Make sure you’re on the latest.

1 Like

Many thanks for the quick reply! I’m using MTK v9.49.0. Below is the full list of versions:

Status `~/.julia/environments/v1.11/Manifest.toml`
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⌅ [fb77eaff] Sundials_jll v5.2.3+0
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Velow is the full jupyter notebook. The issue happens on the last statement: @mtkbuild model_with_lut_model = model_with_lut()

using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
using ModelingToolkitStandardLibrary
using ModelingToolkitStandardLibrary.Blocks
using DataInterpolations
using OrdinaryDiffEq
using DataFrames
using Plots

function MassSpringDamper(; name)
    @named input = RealInput()
    @variables f(t)=0 x(t)=0 dx(t)=0 ddx(t)=0
    @parameters m=10 k=1000 d=1

    eqs = [
           f ~ input.u
           ddx * 10 ~ k * x + d * dx + f
           D(x) ~ dx
           D(dx) ~ ddx]

    ODESystem(eqs, t; name, systems = [input])
end

function MassSpringDamperSystem(data, time; name)
    @named src = ModelingToolkitStandardLibrary.Blocks.Interpolation(LinearInterpolation, data, time)
    @named clk = ContinuousClock()
    @named model = MassSpringDamper()

    eqs = [
        connect(src.input, clk.output)
        connect(src.output, model.input)
    ]

    ODESystem(eqs, t, [], []; name, systems = [src, clk, model])
end

function generate_data()
    dt = 4e-4
    time = 0:dt:0.1
    data = sin.(2 * pi * time * 100)

    return DataFrame(; time, data)
end

df = generate_data() # example data

@named system = MassSpringDamperSystem(df.data, df.time)
sys = structural_simplify(system)
prob = ODEProblem(sys, [], (0, df.time[end]))
sol = solve(prob)
plot(sol)

@mtkmodel model_with_lut begin

    @parameters begin
        table_data = [1.0, 2.0, 3.0]
        table_bkp = [0.0, 0.5, 1.0]
    end

    @components begin
        src = Interpolation(LinearInterpolation, table_data, table_bkp)
        clk = ContinuousClock()
        model = MassSpringDamper()
    end
    @equations begin
        connect(src.input, clk.output)
        connect(src.output, model.input)
    end
end;

@mtkbuild model_with_lut_model = model_with_lut()

It would need the latest ModelingToolkitStandardLibrary.

As per the “manifest” on the post (see below), the MTK Standard Lib is at commit bca6e28, which seems to be the latest for branch “main”.

Oh we were missing a released. That should be fixed in about an hour.

Can DataInterpolations be used to specify things like initial conditions? I tried modifying the Schrödinger Equation example from MethodOfLines.jl to use a LinearInterpolation to construct the initial conditions, and got an error.

The purpose of doing this would be to use model or experiment data to specify the initial state of a system (e.g. number density and temperature of a gas as a function of altitude) and then forward-model the evolution of these state variables.

Here’s the modified example code (errors on discretize step):

using MethodOfLines, OrdinaryDiffEq, Plots, DomainSets, ModelingToolkit
using DataInterpolations

# define a linear interpolation
xs = collect(0.0:0.01:1.0)
ψ0 = LinearInterpolation(sin.(xs.^2), xs)
Tψ0 = typeof(ψ0)

@parameters t, x, (interp::Tψ0)(..)
@variables ψ(..)

Dt = Differential(t)
Dxx = Differential(x)^2

xmin = 0
xmax = 1

V(x) = 0.0

eq = [im * Dt(ψ(t, x)) ~ Dxx(ψ(t, x)) + V(x) * ψ(t, x)] # You must enclose complex equations in a vector, even if there is only one equation

# define ψ0 using interpolator
ψ0 = x -> interp(x)

bcs = [ψ(0, x) ~ ψ0(x),
    ψ(t, xmin) ~ 0,
    ψ(t, xmax) ~ 0]

domains = [t ∈ Interval(0, 1), x ∈ Interval(xmin, xmax)]

@named sys = PDESystem(eq, bcs, domains, [t, x], [ψ(t, x)])

disc = MOLFiniteDifference([x => 100], t)

prob = discretize(sys, disc) # error at this step

sol = solve(prob, TRBDF2(), saveat = 0.01)

I’m using the latest versions of ModelingToolkit, etc:

  [992eb4ea] CondaPkg v0.2.23
  [82cc6244] DataInterpolations v6.5.2
  [5b8099bc] DomainSets v0.7.14
  [f67ccb44] HDF5 v0.17.2
  [a98d9a8b] Interpolations v0.15.1
  [94925ecb] MethodOfLines v0.11.6
  [961ee093] ModelingToolkit v9.49.0
  [16a59e39] ModelingToolkitStandardLibrary v2.17.0
  [8913a72c] NonlinearSolve v3.15.1
  [1dea7af3] OrdinaryDiffEq v6.89.0
  [91a5bcdd] Plots v1.40.8
  [6099a3de] PythonCall v0.9.23
  [53ae85a6] SciMLStructures v1.5.0
  [0c5d862f] Symbolics v6.17.0

That should work now. Open an issue on MethodOfLines.jl’s Github repo and I can check out if it’s MOL specific.

1 Like

Hi Chris,

many thanks for the quick reply again!

I still have the issue, even with MTK Standard Lib v2.17.0. Actually, it seems there was no functional change from commit bca6e28, which I was priviously using, and commit 5ff27c8, which is tagged as v2.17.0; the only change I see is the release version number.

Should the current versions support Interpolation being used as a component inside a @mtkmodel?

It should :sweat_smile:. Open an issue, seems like there’s a bit more going on here and I’ll need to pull it local and look.