Many simple differential equation systems no longer supported

[TorkelE]

This just to work previously, enabling us to deal with differential equations expressed in various formats. However, it seems this has fully been moved to AGPL ModelingToolkit, with no support left for general users?

using ModelingToolkitBase
using ModelingToolkitBase: t_nounits as t, D_nounits as D
@variables X(t)
@parameters p d
eqs = [
    D(X)/2 ~ p - d*X,
]
@mtkbuild ssys = System(eqs, t)

ERROR: ArgumentError: ModelingToolkitBase.jl is unable to simplify such systems. Encountered derivative in RHS of equation 0 ~ p - (1//2)*Differential(t, 1)(X(t)) - d*X(t). Please consider using ModelingToolkit.jl for such systems.

Stacktrace:
 [1] __mtkcompile(sys::System; inputs::OrderedCollections.OrderedSet{…}, outputs::OrderedCollections.OrderedSet{…}, disturbance_inputs::OrderedCollections.OrderedSet{…}, fully_determined::Bool, kwargs::@Kwargs{…})
   @ ModelingToolkitBase C:\Users\Torkel\.julia\packages\ModelingToolkitBase\fjBdh\src\systems\systems.jl:322
 [2] __mtkcompile
   @ C:\Users\Torkel\.julia\packages\ModelingToolkitBase\fjBdh\src\systems\systems.jl:120 [inlined]
 [3] _mtkcompile(sys::System; kwargs::@Kwargs{…})
   @ ModelingToolkitBase C:\Users\Torkel\.julia\packages\ModelingToolkitBase\fjBdh\src\systems\systems.jl:117
 [4] _mtkcompile
   @ C:\Users\Torkel\.julia\packages\ModelingToolkitBase\fjBdh\src\systems\systems.jl:103 [inlined]
 [5] mtkcompile(sys::System; additional_passes::Tuple{}, inputs::Vector{…}, outputs::Vector{…}, disturbance_inputs::Vector{…}, split::Bool, kwargs::@Kwargs{})
   @ ModelingToolkitBase C:\Users\Torkel\.julia\packages\ModelingToolkitBase\fjBdh\src\systems\systems.jl:78
 [6] mtkcompile(sys::System)
   @ ModelingToolkitBase C:\Users\Torkel\.julia\packages\ModelingToolkitBase\fjBdh\src\systems\systems.jl:68
 [7] top-level scope
   @ C:\Users\Torkel\.julia\packages\ModelingToolkitBase\fjBdh\src\deprecations.jl:8
 [8] macro expansion
   @ C:\Users\Torkel\.julia\packages\ModelingToolkitBase\fjBdh\src\systems\abstractsystem.jl:2665 [inlined]
Some type information was truncated. Use `show(err)` to see complete types.

[AayushSabharwal]

XRef #4096 (comment). If there's ways to relax this requirement, I'm open to suggestions.

[ChrisRackauckas]

Yingbo was always pretty adamant that's not possible, because choosing what to have on the left hand side is equivalent to an entire matching algorithm, which is then all of the complexity coming in.

[TorkelE]

I agree that there are complciated general cases where this might not be possible, however, I think it would make sense to allow things like this which is really straightforward. I.e. for this example I can strightforwardly generate the correct equation through

eq_input = D(X)/2 ~ p - d*X
eq_processed = D(X) ~ solve_for(eq_input, D(X))

and these are also the kind of equations we are testing for in Catalyst. I could implement a simple routine in Catalyst which performs this operation on all equations, however, it feels like something which belongs in MTKBase and not Catalyst.

[ChrisRackauckas]

In the case where there is one term and it's linear, we could try doing the linear solve_for.

[AayushSabharwal]

So we want to accept equations where the highest degree derivative is the only variable on the LHS, if it can be linearly solved for?

[ChrisRackauckas]

that's fine