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Top 23 differential-equation 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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gosl
Linear algebra, eigenvalues, FFT, Bessel, elliptic, orthogonal polys, geometry, NURBS, numerical quadrature, 3D transfinite interpolation, random numbers, Mersenne twister, probability distributions, optimisation, 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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SciMLBook
Parallel Computing and Scientific Machine Learning (SciML): Methods and Applications (MIT 18.337J/6.338J)
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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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diffrax
Numerical differential equation solvers in JAX. Autodifferentiable and GPU-capable. https://docs.kidger.site/diffrax/
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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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WorkOS
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DiffEqFlux.jl
Pre-built implicit layer architectures with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods
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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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NeuralCDE
Code for "Neural Controlled Differential Equations for Irregular Time Series" (Neurips 2020 Spotlight)
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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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AMaDiA
Astus' Mathematical Display Application : A GUI for Mathematics (Calculator, LaTeX Converter, Plotter, ... )
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SaaSHub
SaaSHub - Software Alternatives and Reviews. SaaSHub helps you find the best software and product alternatives
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.
What about the other benchmarks on the same site? https://docs.sciml.ai/SciMLBenchmarksOutput/stable/Bio/BCR/ BCR takes about a hundred seconds and is pretty indicative of systems biological models, coming from 1122 ODEs with 24388 terms that describe a stiff chemical reaction network modeling the BCR signaling network from Barua et al. Or the discrete diffusion models https://docs.sciml.ai/SciMLBenchmarksOutput/stable/Jumps/Dif... which are the justification behind the claims in https://www.biorxiv.org/content/10.1101/2022.07.30.502135v1 that the O(1) scaling methods scale better than O(log n) scaling for large enough models? I mean.
> If you use special routines (BLAS/LAPACK, ...), use them everywhere as the respective community does.
It tests with and with BLAS/LAPACK (which isn't always helpful, which of course you'd see from the benchmarks if you read them). One of the key differences of course though is that there are some pure Julia tools like https://github.com/JuliaLinearAlgebra/RecursiveFactorization... which outperform the respective OpenBLAS/MKL equivalent in many scenarios, and that's one noted factor for the performance boost (and is not trivial to wrap into the interface of the other solvers, so it's not done). There are other benchmarks showing that it's not apples to apples and is instead conservative in many cases, for example https://github.com/SciML/SciPyDiffEq.jl#measuring-overhead showing the SciPyDiffEq handling with the Julia JIT optimizations gives a lower overhead than direct SciPy+Numba, so we use the lower overhead numbers in https://docs.sciml.ai/SciMLBenchmarksOutput/stable/MultiLang....
> you must compile/write whole programs in each of the respective languages to enable full compiler/interpreter optimizations
You do realize that a .so has lower overhead to call from a JIT compiled language than from a static compiled language like C because you can optimize away some of the bindings at the runtime right? https://github.com/dyu/ffi-overhead is a measurement of that, and you see LuaJIT and Julia as faster than C and Fortran here. This shouldn't be surprising because it's pretty clear how that works?
I mean yes, someone can always ask for more benchmarks, but now we have a site that's auto updating tons and tons of ODE benchmarks with ODE systems ranging from size 2 to the thousands, with as many things as we can wrap in as many scenarios as we can wrap. And we don't even "win" all of our benchmarks because unlike for you, these benchmarks aren't for winning but for tracking development (somehow for Hacker News folks they ignore the utility part and go straight to language wars...).
If you have a concrete change you think can improve the benchmarks, then please share it at https://github.com/SciML/SciMLBenchmarks.jl. We'll be happy to make and maintain another.
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.
differential-equations related posts
- 2023 was the year that GPUs stood still
- Julia GPU-based ODE solver 20x-100x faster than those in Jax and PyTorch
- [P] Optimistix, nonlinear optimisation in JAX+Equinox!
- Show HN: Optimistix: Nonlinear Optimisation in Jax+Equinox
- Automatically install huge number of dependency?
- Good linear algebra libraries
- Julia 1.9: A New Era of Performance and Flexibility
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A note from our sponsor - WorkOS
workos.com | 29 Apr 2024
Index
What are some of the best open-source differential-equation projects? This list will help you:
Project | Stars | |
---|---|---|
1 | DifferentialEquations.jl | 2,756 |
2 | gosl | 1,806 |
3 | SciMLBook | 1,790 |
4 | torchsde | 1,468 |
5 | ModelingToolkit.jl | 1,335 |
6 | diffrax | 1,230 |
7 | NeuralPDE.jl | 903 |
8 | DiffEqFlux.jl | 837 |
9 | SciMLTutorials.jl | 708 |
10 | NeuralCDE | 581 |
11 | OrdinaryDiffEq.jl | 498 |
12 | diffeqpy | 496 |
13 | Catalyst.jl | 421 |
14 | DataDrivenDiffEq.jl | 398 |
15 | vsl | 328 |
16 | Surrogates.jl | 314 |
17 | SciMLSensitivity.jl | 311 |
18 | 18S096SciML | 303 |
19 | DiffEqBase.jl | 297 |
20 | SciMLBenchmarks.jl | 290 |
21 | ComponentArrays.jl | 276 |
22 | DiffEqGPU.jl | 267 |
23 | AMaDiA | 260 |
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