Gridap.jl
DiffEqOperators.jl
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| Gridap.jl | DiffEqOperators.jl | |
|---|---|---|
| 2 | 3 | |
| 635 | 281 | |
| 1.6% | - | |
| 9.2 | 4.6 | |
| 5 days ago | 10 months ago | |
| Julia | Julia | |
| MIT License | GNU General Public License v3.0 or later |
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Gridap.jl
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Best free/open source CAS ?
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.
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[Research] Input Arbitrary PDE -> Output Approximate Solution
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.
DiffEqOperators.jl
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Julia 1.7 has been released
>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.
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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.
(b) DiffEqOperators.jl is being worked on https://github.com/SciML/DiffEqOperators.jl/pull/467 .
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What's Bad about Julia?
I like that they are colored now, but really what needs to be added is type parameter collapasing. In most cases, you want to see `::Dual{...}`, i.e. "it's a dual number", not `::Dual{typeof(ODESolution{sfjeoisjfsfsjslikj},sfsef,sefs}` (these can literally get to 3000 characters long). As an example of this, see the stacktraces in something like https://github.com/SciML/DiffEqOperators.jl/issues/419 . The thing is that it gives back more type information than the strictest dispatch: no function is dispatching off of that first 3000 character type parameter, so you know that printing that chunk of information is actually not informative to any method decisions. Automated type abbreviations could take that heuristic and chop out a lot of the cruft.
What are some alternatives?
dolfinx - Next generation FEniCS problem solving environment
BoundaryValueDiffEq.jl - Boundary value problem (BVP) solvers for scientific machine learning (SciML)
DifferentialEquations.jl - Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.
FourierFlows.jl - Tools for building fast, hackable, pseudospectral partial differential equation solvers on periodic domains
ModelingToolkit.jl - An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and automated transformations of differential equations
ApproxFun.jl - Julia package for function approximation
SciMLTutorials.jl - Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.
oxide-enzyme - Enzyme integration into Rust. Experimental, do not use.
NeuralPDE.jl - Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
julia - The Julia Programming Language