scientific-machine-learning

If I run the copy&paste examples, such as https://mtk.sciml.ai/stable/tutorials/acausal_components/ :

using ModelingToolkit, Plots, DifferentialEquations

@variables t
@connector function Pin(;name)
    sts = @variables v(t)=1.0 i(t)=1.0 [connect = Flow]
    ODESystem(Equation[], t, sts, []; name=name)
end

function Ground(;name)
    @named g = Pin()
    eqs = [g.v ~ 0]
    

https://arxiv.org/abs/2012.06684

@samuela is there code to share that could become a tutorial? I think it would be good to make one.

add in docs and in testset a Low-level API example with GPU

At the moment the nla() function takes an array as input and returns the modified array as output, but this creates a lot of allocations inside for loops. The new function call nla!() should take in the array to be modified and a preallocated array to store the modified array in. This should remove unneeded allocations and speed up computations.