Heterogeneous units and ModelingToolkit

Specific Domains Modelling & Simulations
1

I am trying to use the ModelingToolkit together with Unitful to model a coupled system of two ODEs with different units. The following code fails on ODEProblem with a DimensionError unless both units in u0 are the same:

using ModelingToolkit
using DifferentialEquations
using Plots
using Unitful
@parameters t k1 k2
@variables y(t) z(t)
@derivatives D'~t
eqs = [D(y) ~ k1*y, D(z) ~ k2*z]
de = ODESystem(eqs)
u0 = [y => 1.5u"V", z => 3.1u"N"]
p = [k1 => 1.0u"1/s", k2 => 1.0u"1/s"]
tspan = (0.0u"s",1e-5u"s")
prob = ODEProblem(de,u0,tspan, p, jac=false) # ERROR: DimensionError: V and 3.1 N are not dimensionally compatible.
sol = solve(prob, Euler(), dt=1e-6u"s")

I know that heterogeneous variables are an issue, as discussed here: DifferentialEquations.jl and systems with heterogenous units
The problem in that case was the adaptive stepping that can’t calculate a vector norm if the vector has heterogeneous units.
The suggested solution was to use ArrayPartition:
ODE systems with heterogenous units · Issue #147 · SciML/DifferentialEquations.jl · GitHub

It suspect that I am running into a similar problem, even though in my case the code fails at ODEProblem(), not on solve().

What is the best approach to use units in my case?

2

The solution here is to type the variables and generate the code as un-united. This isn’t documented yet but will be documented once the front end part of it is ready.

3

Thanks, Chris!

4

Did you get this working, if so, would you post your code?

5

I didn’t get it to work, but I haven’t checked the latest versions. At the time, it still needed some changes to ModelingToolkit.

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6

We still want to finish the union of SymbolicUtils and MTK first before heading back and making an interface to the unit parts (which exist, but are buried)

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