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Top 23 Ode Open-Source Projects
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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.
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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
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InfluxDB
Power Real-Time Data Analytics at Scale. Get real-time insights from all types of time series data with InfluxDB. Ingest, query, and analyze billions of data points in real-time with unbounded cardinality.
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NeuralPDE.jl
Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
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SciMLTutorials.jl
Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.
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OrdinaryDiffEq.jl
High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)
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diffeqpy
Solving differential equations in Python using DifferentialEquations.jl and the SciML Scientific Machine Learning organization
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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.
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DataDrivenDiffEq.jl
Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization
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SciMLSensitivity.jl
A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.
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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
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SciMLBenchmarks.jl
Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R
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DiffEqGPU.jl
GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem
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auto-07p
AUTO is a publicly available software for continuation and bifurcation problems in ordinary differential equations originally written in 1980 and widely used in the dynamical systems community.
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DiffEqDevTools.jl
Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)
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The documentation has a manifest associated with it: https://docs.sciml.ai/NeuralPDE/dev/#Reproducibility. Instantiating the manifest will give you all of the exact versions used for the documentation build (https://github.com/SciML/NeuralPDE.jl/blob/gh-pages/v5.7.0/assets/Manifest.toml). You just ]instantiate folder_of_manifest. Or you can use the Project.toml.
There has been a lot of research in Runge Kutta methods in the last couple decades which resulted in all kind of specialized Runge Kutta methods. You have high order ones, RK methods for stiff problems, embedded RK methods which benefit from adaprive step size control, RK-Nystrom methods for second order Problems, symplectic RK methods which preserve energy (eg. hamiltonian) ando so on. If you are interested in the numerics and the use cases I highly recommend checking out the Julia Libary OrdinaryDiffEq (https://github.com/SciML/OrdinaryDiffEq.jl). If you look into the documentation you find A LOT of implemented RK methods for all kind of use cases.
Indeed, and this year we created a system for compiling ODE code not just optimized CUDA kernels but also OneAPI kernels, AMD GPU kernels, and Metal. Peer reviewed version is here (https://www.sciencedirect.com/science/article/abs/pii/S00457...), open access is here (https://arxiv.org/abs/2304.06835), and the open source code is at https://github.com/SciML/DiffEqGPU.jl. The key that the paper describes is that in this case kernel generation is about 20x-100x faster than PyTorch and Jax (see the Jax compilation in multiple ways in this notebook https://colab.research.google.com/drive/1d7G-O5JX31lHbg7jTzz..., extra overhead though from calling Julia from Python but still shows a 10x).
The point really is that while deep learning libraries are amazing, at the end of the day they are DSL and really pull towards one specific way of computing and parallelization. It turns out that way of parallelizing is good for deep learning, but not for all things you may want to accelerate. Sometimes (i.e. cases that aren't dominated by large linear algebra) building problem-specific kernels is a major win, and it's over-extrapolating to see ML frameworks do well with GPUs and think that's the only thing that's required. There are many ways to parallelize a code, ML libraries hardcode a very specific way, and it's good for what they are used for but not every problem that can arise.
Project mention: Julia as a unifying end-to-end workflow language on the Frontier exascale system | news.ycombinator.com | 2023-11-19
Project mention: auto-07p VS BifurcationKit.jl - a user suggested alternative | libhunt.com/r/auto-07p | 2024-02-11
Project mention: What numerical libraries (besides LAPACK) do you normally use in Fortran? | /r/fortran | 2023-06-09I have used many codes by John Burkardt https://people.sc.fsu.edu/~jburkardt/f_src/f_src.html and classified them at https://github.com/Beliavsky/Burkardt-Fortran-90 .
NOTE:
The open source projects on this list are ordered by number of github stars.
The number of mentions indicates repo mentiontions in the last 12 Months or
since we started tracking (Dec 2020).
Ode related posts
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auto-07p VS BifurcationKit.jl - a user suggested alternative
2 projects | 11 Feb 2024 -
2023 was the year that GPUs stood still
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Julia as a unifying end-to-end workflow language on the Frontier exascale system
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Modern Numerical Solving methods
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Why Fortran is a scientific powerhouse
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Mathematically Modelling a PRV
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How Julia ODE Solve Compile Time Was Reduced From 30 Seconds to 0.1
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A note from our sponsor - SaaSHub
www.saashub.com | 11 May 2024
Index
What are some of the best open-source Ode projects? This list will help you:
| Project | Stars | |
|---|---|---|
| 1 | DifferentialEquations.jl | 2,761 |
| 2 | ModelingToolkit.jl | 1,338 |
| 3 | NeuralPDE.jl | 905 |
| 4 | SciMLTutorials.jl | 709 |
| 5 | Latexify.jl | 531 |
| 6 | OrdinaryDiffEq.jl | 503 |
| 7 | diffeqpy | 497 |
| 8 | Catalyst.jl | 422 |
| 9 | DataDrivenDiffEq.jl | 398 |
| 10 | SciMLSensitivity.jl | 311 |
| 11 | DiffEqBase.jl | 297 |
| 12 | SciMLBenchmarks.jl | 292 |
| 13 | DiffEqGPU.jl | 267 |
| 14 | SciMLStyle | 196 |
| 15 | heyoka | 190 |
| 16 | ode4j | 156 |
| 17 | auto-07p | 114 |
| 18 | ModelingToolkitStandardLibrary.jl | 98 |
| 19 | heyoka.py | 58 |
| 20 | odex-js | 53 |
| 21 | DiffEqDevTools.jl | 46 |
| 22 | Burkardt-Fortran-90 | 39 |
| 23 | godesim | 23 |
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