Some minor clarifications: NeuralODEs are not a Julia invention. I am pretty sure the first papers on the topic were using a python package implementing a rather crude ODE solver in torch or tensorflow. Julia just happens to be light years ahead of any other tool when it comes to solving ODEs, while having many high-quality autodifferentiation packages as well, so it feels natural to use it for these problems. But more importantly, SciML is not just for your typical Machine Learning tasks: being able to solve ODEs and have autodiff over them is incredibly empowering for boring old science and engineering, and SciML has become one of the most popular set of libraries when it comes to unwieldy ODEs.

What do you mean by "more" people? Perhaps you mean people who know? Anyone who solves a differential equation in Julia is using the SciML ecosystem of packages. The Julia ecosystem is about 1M users, and lots of people in that ecosystem use these tools.

There's over 100 dependent packages: https://juliahub.com/ui/Packages/OrdinaryDiffEq/DlSvy/5.64.1...

> Why is it limited to a small group of Julia developers and packages?

I don't think there are any gatekeepers limiting it's use. Articles like the one highlighted here help to get the word out to more potential users.

Lots to say here. First of all, the community growth has been pretty tremendous and I couldn't really ask for more. We're seeing tens of thousands of visitors to the documentation of various packages, and have some high profile users. For example, NASA showing a 15,000x acceleration (https://www.youtube.com/watch?v=tQpqsmwlfY0) and the Head of Clinical Pharmacology at Moderna saying SciML-based Pumas "has emerged as our 'go-to' tool for most of our analyses in recent months" in 2020 (see https://pumas.ai/). We try to keep a showcase (https://sciml.ai/showcase/) but at this point it's hard to stay on top of the growth. I think anyone would be excited to see an open source side project reach that level of use. Since we tend to focus on core numerical issues (stiffness) and performance, we target the more "hardcore" people in scientific disciplines who really need these aspects and those communities are the ones seeing the most adoption (pharmacology, systems biology, combustion modeling, etc.). Indeed the undergrad classes using a non-stiff ODE solver on small ODEs or training a neural ODE on MNIST don't really have those issues so they aren't our major growth areas. That's okay and that's probably the last group that would move.

In terms of the developer team, throughout the SciML organization repositories we have had around 30 people who have had over 100 commits, which is similar in number to NumPy and SciPy. Julia naturally has a much lower barrier to entry in terms of committing to such packages (since the packages are all in Julia rather than C/Fortran), so the percentage of users who become developers is much higher which is probably why you see a lot more developer activity in contrast to "pure" users. With things like the Python community you have a group of people who write blog posts and teach the tools in courses without ever hacking on the packages or its ecosystem. In Julia, that background is sufficient knowledge to also be developing the package, so everyone writing about Julia seems to also be associated with developing Julia packages somehow. I tend to think that's a positive, but it does make the community look insular as everyone you see writing about Julia is also a developer of packages.

Lastly, since we have been focusing on people with big systems and numerically hard problems, we have had the benefit of being able to overlook some "simple user" issues so far. We are starting to do a big push to clean up things like compile times (https://github.com/SciML/DifferentialEquations.jl/issues/786), improve the documentation, throw better errors, support older versions longer, etc. One way to think about SciML is that it's somewhat the Linux to the monolith Python packages's Windows. We give modular tools in a bunch of different packages that work together, get high performance, and become "more than the sum of the parts", but sometimes people are fine with the simple app made for one purpose. With DEQs, there's a Python package specifically for DEQs (https://github.com/locuslab/deq). Does it have all of the Newton-Krylov choices for the different classes of Jacobians and all of that? No, but it gets something simple and puts an easily Google-able face to it. So while all it takes in Julia with SciML is to stick a nonlinear solver in the right spot in the right way and know how the adjoint codegen will bring it all together, the majority want Visual Studio instead of Awk+Sed or Vim. We understand that, and so the DiffEqFlux.jl package is essentially just a repository of tutorials and prebuilt architectures that people tend to want (https://diffeqflux.sciml.ai/dev/) but we need to continue improving that "simplified experience". The age of Linux is more about making desktop managers that act sufficiently like Windows and less about trying to get everyone building ArchLinux from source. Right now we are currently too much like ArchLinux and need to build more of the Ubuntu-like pieces. We thus have similarly loyal hardcore followers but need to focus a bit on making that installation process easier and the error messages shorter to attract a larger crowd.