Top 10 Julia partialdifferentialequation Projects

DifferentialEquations.jl
Multilanguage suite for highperformance solvers of differential equations and scientific machine learning (SciML) components
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,

DiffEqFlux.jl
Universal neural differential equations with O(1) backprop, GPUs, and stiff+nonstiff DE solvers, demonstrating scientific machine learning (SciML) and physicsinformed machine learning methods

SonarLint
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NeuralPDE.jl
PhysicsInformed Neural Networks (PINN) and Deep BSDE Solvers of Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
PDE solving libraries are MethodOfLines.jl and NeuralPDE.jl. NeuralPDE is very general but not very fast (it's a limitation of the method, PINNs are just slow). MethodOfLines is still somewhat under development but generates quite fast code.

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.


DiffEqOperators.jl
Linear operators for discretizations of differential equations and scientific machine learning (SciML)
>I hope those benchmarks are coming in hot
M1 is extremely good for PDEs because of its large cache lines.
https://github.com/SciML/DiffEqOperators.jl/issues/407#issue...
The JuliaSIMD tools which are internally used for BLAS instead of OpenBLAS and MKL (because they tend to outperform standard BLAS's for the operations we use https://github.com/YingboMa/RecursiveFactorization.jl/pull/2...) also generate good code for M1, so that was giving us some powerful use cases right off the bat even before the heroics allowed C/Fortran compilers to fully work on M1.

SciMLBenchmarks.jl
Benchmarks for scientific machine learning (SciML) software, scientific AI, and (differential) equation solvers
> But in the end, it's FORTRAN all the way down. Even in Julia.
That's not true. None of the Julia differential equation solver stack is calling into Fortran anymore. We have our own BLAS tools that outperform OpenBLAS and MKL in the instances we use it for (mostly LUfactorization) and those are all written in pure Julia. See https://github.com/YingboMa/RecursiveFactorization.jl, https://github.com/JuliaSIMD/TriangularSolve.jl, and https://github.com/JuliaLinearAlgebra/Octavian.jl. And this is one part of the DiffEq performance story. The performance of this of course is all validated on https://github.com/SciML/SciMLBenchmarks.jl

Scout APM
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DiffEqBase.jl
The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
Project mention: Simulating a simple circuit with the ModelingToolkit  reddit.com/r/Julia  20220629 
FourierFlows.jl
Tools for building fast, hackable, pseudospectral partial differential equation solvers on periodic domains

PDE solving libraries are MethodOfLines.jl and NeuralPDE.jl. NeuralPDE is very general but not very fast (it's a limitation of the method, PINNs are just slow). MethodOfLines is still somewhat under development but generates quite fast code.
Julia partialdifferentialequations related posts
 Best free/open source CAS ?
 Chebfun – Numerical Computing with Functions
 Why are NonlinearSolve.jl and DiffEqOperators.jl incompatible with the latest versions of ModelingToolkit and Symbolics!!!? Symbolics and ModelingToolkit are heavily downgraded when those packages are added.
 [Research] Input Arbitrary PDE > Output Approximate Solution
Index
What are some of the best opensource partialdifferentialequation projects in Julia? This list will help you:
Project  Stars  

1  DifferentialEquations.jl  2,332 
2  DiffEqFlux.jl  720 
3  NeuralPDE.jl  646 
4  Gridap.jl  443 
5  ApproxFun.jl  440 
6  DiffEqOperators.jl  264 
7  SciMLBenchmarks.jl  225 
8  DiffEqBase.jl  203 
9  FourierFlows.jl  128 
10  MethodOfLines.jl  84 
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