ReservoirComputing.jl VS DifferentialEquations.jl

Not just similar, the same. If you look through the documentation you'll see that https://github.com/SciML/ReservoirComputing.jl is a collection of reservoir architectures with high performance implementations, and some of our recent research has been pulling reservoir computing to the continuous domain for stiff ODEs (think of it almost like a neural ODE that you do not need to train via gradient descent): https://arxiv.org/abs/2010.04004 . We are definitely digging through this paper with some fascination and will incorporate a lot of its advancements into the software.

Another up-and-coming solution is Julia's simulation ecosystem [1]. It is powered by the commercial organization behind the Julia programming language, which has received DARPA funding [2] to build out these tools. This ecosystem unifies researchers in numerical methods [3], scalable compute, and domain experts in modeling engineering systems (electrical, mechanical, etc.) I believe this is where simulation is headed.

[1] https://juliahub.com/products/juliasim

[2] https://news.ycombinator.com/item?id=26425659

[3] https://docs.sciml.ai/DiffEqDocs/stable/

This lists some of its unique abilities:

https://docs.sciml.ai/DiffEqDocs/stable/

The routines are sufficiently generic, with regard to Julia’s type system, to allow the solvers to automatically compose with other packages and to seamlessly use types other than Numbers. For example, instead of handling just functions Number→Number, you can define your ODE in terms of quantities with physical dimensions, uncertainties, quaternions, etc., and it will just work (for example, propagating uncertainties correctly to the solution¹). Recent developments involve research into the automated selection of solution routines based on the properties of the ODE, something that seems really next-level to me.

[1] https://lwn.net/Articles/834571/

https://github.com/SciML/DifferentialEquations.jl/issues/786. As you could see from the tweet, it's now at 0.1 seconds. That has been within one year.

Also, if you take a look at a tutorial, say the tutorial video from 2018,

It's not faith, and it's not all from Julia itself. https://github.com/SciML/DifferentialEquations.jl/issues/785 should reduce compile times of what OP mentioned for example.

Let's even put raw numbers to it. DifferentialEquations.jl usage has seen compile times drop from 22 seconds to 3 seconds over the last few months.

https://github.com/SciML/DifferentialEquations.jl/issues/786

https://github.com/SciML/DifferentialEquations.jl/issues/737 double posted, with the answer here. Please don't do that.