MomentClosure.jl
DifferentialEquations.jl
MomentClosure.jl | DifferentialEquations.jl | |
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1 | 6 | |
43 | 2,761 | |
- | 0.9% | |
5.6 | 7.2 | |
3 months ago | 6 days ago | |
Julia | Julia | |
MIT License | GNU General Public License v3.0 or later |
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MomentClosure.jl
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Should I switch over completely to Julia from Python for numerical analysis/computing?
ModelingToolkit.jl adds a different spin on this by noting what makes a good modeling system isn't top down but a system that allows for bottom up contributions. ModelingToolkit is built on Symbolics.jl which uses OSCAR.jl etc., so every time the symbolics community gets better ModelingToolkit.jl gets better. It connects to the whole SciML ecosystem, so any improvement to any of the SciML interface packages is directly an improvement to ModelingToolkit.jl. ModelingToolkit is made to be a set of composable compiler abstractions called transformations, so anyone can add new packages that do new transformations that improve the ecosystem. One that I really like is MomentClosure.jl which symbolically transforms stochastic ModelingToolkit models (ReactionSystem) to approximate symbolic ODESystem models of the moments. And there's domain-specific langauges like Catalyst.jl being built on the interface to give more ways to build models, which is spawning the biocommunity to make model importers into the symbolic forms, when then feeds more ODE models into the same compiler. JuliaSim is then building on this ecosystem, adding cloud infrastructure that is special-purpose made for doing parallel computations of these models, automatic symbolic model discovery from data, automatic generation of approximate models with machine learning, and tying the Julia Computing compiler team into the web that is building this ecosystem.
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?
Catalyst.jl - Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.
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
casadi - CasADi is a symbolic framework for numeric optimization implementing automatic differentiation in forward and reverse modes on sparse matrix-valued computational graphs. It supports self-contained C-code generation and interfaces state-of-the-art codes such as SUNDIALS, IPOPT etc. It can be used from C++, Python or Matlab/Octave.
diffeqpy - Solving differential equations in Python using DifferentialEquations.jl and the SciML Scientific Machine Learning organization
Causal.jl - Causal.jl - A modeling and simulation framework adopting causal modeling approach.
Gridap.jl - Grid-based approximation of partial differential equations in Julia
ApproxFun.jl - Julia package for function approximation
DiffEqBase.jl - The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
FFTW.jl - Julia bindings to the FFTW library for fast Fourier transforms
CUDA.jl - CUDA programming in Julia.
SciMLBenchmarks.jl - Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R
ReservoirComputing.jl - Reservoir computing utilities for scientific machine learning (SciML)