Gridap.jl
DifferentialEquations.jl
| Gridap.jl | DifferentialEquations.jl | |
|---|---|---|
| 2 | 6 | |
| 716 | 2,875 | |
| 0.8% | 0.5% | |
| 9.5 | 6.9 | |
| 5 days ago | 27 days 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.
DifferentialEquations.jl
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Startups are building with the Julia Programming Language
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/
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From Common Lisp to Julia
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,
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When is julia getting proper precompilation?
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.
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Julia 1.7 has been released
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
- Suggest me a Good library for scientific computing in Julia with good support for multi-core CPUs and GPUs.
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DifferentialEquations compilation issue in Julia 1.6
https://github.com/SciML/DifferentialEquations.jl/issues/737 double posted, with the answer here. Please don't do that.
What are some alternatives?
dolfinx - Next generation FEniCS problem solving environment
diffeqpy - Solving differential equations in Python using DifferentialEquations.jl and the SciML Scientific Machine Learning organization
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
DiffEqOperators.jl - Linear operators for discretizations of differential equations and scientific machine learning (SciML)
DiffEqBase.jl - The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
FourierFlows.jl - Tools for building fast, hackable, pseudospectral partial differential equation solvers on periodic domains
FFTW.jl - Julia bindings to the FFTW library for fast Fourier transforms
NeuralPDE.jl - Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
ReservoirComputing.jl - Reservoir computing utilities for scientific machine learning (SciML)