Gridap.jl VS julia

Another I've been working on learning is Julia, which aims to use a syntax very similar to how you'd write it mathematically, and I like being able to include units in calculations using the unitful.jl package, and there are FEM packages available like Gridap.

PINN methods are absurdly slow (DeepXDE is about 10,000x slower than an ODE solver for example, while using implicit parallelism vs serial ODE solver) but they are flexible. So ModelingToolkit.jl has alternative options, like DiffEqOperators.jl takes the same specification and generates ODESystem and NonlinearSystem problems via finite difference discretizations (known as "method of lines"). There's a (pseudo-)spectral part of the interface coming relatively soon as well, with GridAP.jl integration for FEM coming soon. So this is made to be a universal arbitrary PDE -> approximate solution interface which is generic to the method and solving process.

_ __ _(_)_ | Documentation: https://docs.julialang.org (_) | (_) (_) | _ _ _| |_ __ _ | Type "?" for help, "]?" for Pkg help. | | | | | | |/ _` | | | | |_| | | | (_| | | Version 1.11.2 (2024-12-01) _/ |\__'_|_|_|\__'_| | Official https://julialang.org/ release |__/ | julia>

The paper examines the current state of the Julia programming language for scientific machine learning (SML). Julia is a relatively new language that is designed to be fast, easy to use, and well-suited for scientific and numerical computing.

Download and Install Julia: Head over to https://julialang.org/ and download the appropriate installer for your operating system. Follow the installation instructions.

The above two steps is only for getting warm up, now you need to start coding on a programming language. Most of the AI community uses Python and there are other programming languages like Julia which is similar to python but it is faster than python, R used for statistical analysis and data visualization. Just try to learn one programming language with the Data Structure and Algorithm(DSA) and Object Oriented Programming System (OOPS) concepts.

If you are not writing the GPU kernel, just use a high level language which wraps up the CUDA, Metal, or whatever.

https://julialang.org

It also turns out that it allows for a bunch more compiler optimizations to be implimented with a lot less pain. I got very nerd sniped on this this week leading to https://github.com/JuliaLang/julia/pull/56030 and https://github.com/JuliaLang/julia/pull/55913 which allow allocation removal in a number of cases and saves ~4ns (~10ns->6ns for Memory{Int8}(unef, 4)) for constructing Memory objects.

Julia, renowned for its speed and efficiency in scientific computing, has caught the eye of many in the data science world. We were eager to find out if there's real power behind the hype. Curious about whether JuliaLang lives up to its reputation as the sprinter of the programming world?

> are not an issue with Julia (eg memory safety)

Note that Julia does allow memory unsafety, for example you can mark array accesses with `@inbounds` to remove bound checks, kinda like how you can use `unsafe` in Rust except it looks much less scary.

It also doesn't help that the official example for how to use it safe was actually not safe [1]. Granted, this is just a single example and has been fixed since then, but it doesn't give a nice impression of their mindset when dealing with memory safety.

More in general there doesn't seem to be a strong mindset for correctness either. See [2] for a collection of such issues.

[1]: https://github.com/JuliaLang/julia/issues/39367

[2]: https://yuri.is/not-julia/

A couple years ago, I came across a language called Julia. It's multiple dispatch feature was very interesting; I wanted to know how it worked under the hood, but I didn't have the knowledge to do that yet. So here I am, finally giving it a try. Now that I have an implementation, I realized there is nothing tying this algorithm to runtime dispatch; I think it could be used in a language with static dispatch as well. If you're interested in learning about multiple dispatch, I left some links at the end of the post. So I guess this post is just about selecting the most specific function for a given set of arguments in a language with subtyping. Ok, let's get started.