DifferentialEquations.jl extensions

[MilesCranmer]

@gaurav-arya this is an attempt to get DifferentialEquations.jl working. @ChrisRackauckas got part of the way on this issue: https://github.com/SciML/DifferentialEquations.jl/issues/993#issuecomment-1785034821

[github-actions[bot]]

Benchmark Results

	main	8e03c10916438e...	t[main]/t[8e03c10916438e...]
Quantity/creation/Quantity(x)	2.79 ± 0.01 ns	2.79 ± 0.01 ns	1
Quantity/creation/Quantity(x, length=y)	4.02 ± 0.01 ns	3.11 ± 0.01 ns	1.29
Quantity/with_numbers/*real	3.1 ± 0.01 ns	3.1 ± 0.01 ns	1
Quantity/with_numbers/^int	7.74 ± 1.8 ns	7.74 ± 1.8 ns	1
Quantity/with_numbers/^int * real	7.75 ± 1.9 ns	7.75 ± 1.9 ns	1
Quantity/with_quantity/+y	5.27 ± 0.01 ns	5.27 ± 0.01 ns	1
Quantity/with_quantity//y	3.41 ± 0.01 ns	3.41 ± 0.01 ns	1
Quantity/with_self/dimension	1.55 ± 0.01 ns	1.55 ± 0.01 ns	1
Quantity/with_self/inv	3.11 ± 0.01 ns	3.11 ± 0.01 ns	1
Quantity/with_self/ustrip	1.55 ± 0.01 ns	1.55 ± 0.01 ns	1
QuantityArray/broadcasting/multi_array_of_quantities	0.149 ± 0.14 ms	0.149 ± 0.14 ms	0.998
QuantityArray/broadcasting/multi_normal_array	0.05 ± 0.00034 ms	0.05 ± 0.00025 ms	1
QuantityArray/broadcasting/multi_quantity_array	0.159 ± 0.0017 ms	0.159 ± 0.0019 ms	1
QuantityArray/broadcasting/x^2_array_of_quantities	27.8 ± 2.1 μs	27.6 ± 2.1 μs	1.01
QuantityArray/broadcasting/x^2_normal_array	5.88 ± 0.76 μs	5.9 ± 0.82 μs	0.997
QuantityArray/broadcasting/x^2_quantity_array	6.25 ± 0.4 μs	6.27 ± 0.39 μs	0.997
QuantityArray/broadcasting/x^4_array_of_quantities	0.0789 ± 0.00066 ms	0.0788 ± 0.00058 ms	1
QuantityArray/broadcasting/x^4_normal_array	0.0469 ± 0.00021 ms	0.0469 ± 0.00021 ms	1
QuantityArray/broadcasting/x^4_quantity_array	0.0563 ± 0.00025 ms	0.0563 ± 0.00023 ms	0.999
time_to_load	0.168 ± 0.00067 s	0.168 ± 0.0081 s	0.999

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR. Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

[ChrisRackauckas]

I think you'll need a few changes to OrdinaryDiffEq.jl itself. Also, we'll need to think about how some things like scalar tolerances are handled if there's multiple different units, that needs some representation like a fillvector just for the units

[MilesCranmer]

By multiple different units do you mean if the user were to use SymbolicDimensions, which let's you choose cm or m for storing length? The default Dimensions type enforces SI units (i.e., no prefixes) everywhere; will that be an issue?