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Top 21 partial-differential-equation Open-Source Projects
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Financial-Models-Numerical-Methods
Collection of notebooks about quantitative finance, with interactive python code.
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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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NeuralPDE.jl
Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
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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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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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FourierFlows.jl
Tools for building fast, hackable, pseudospectral partial differential equation solvers on periodic domains
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pyclaw
PyClaw is a Python-based interface to the algorithms of Clawpack and SharpClaw. It also contains the PetClaw package, which adds parallelism through PETSc.
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nvidia-modulus-airfoil-optimisation
Using NVIDIA modulus for airfoil optimizations at different angles.
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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.
Project mention: [P] LagrangeBench: A Lagrangian Fluid Mechanics Benchmarking Suite | /r/MachineLearning | 2023-12-11LagrangeBench is a machine learning benchmarking library for CFD particle problems based on JAX. It is designed to evaluate and develop learned particle models (e.g. graph neural networks) on challenging physical problems. To our knowledge it's the first benchmark for this specific set of problems. Our work was inspired by the grid-based benchmarks of PDEBench and PDEArena, and we propose it as a Lagrangian alternative.
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.
Example comes from here: https://github.com/bueler/p4pdes/tree/master/c/ch1
I wrote a library called QuantPDE when I was a graduate student that might have what you need. There is a tutorial on the GitHub page for how to implement a Bermudan option with discrete dividends.
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).
partial-differential-equations related posts
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- Eighty Years of the Finite Element Method: Birth, Evolution, and Future
- Best Python package(s) to solve PDEs numerically?
- Best free/open source CAS ?
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Index
What are some of the best open-source partial-differential-equation projects? This list will help you:
| Project | Stars | |
|---|---|---|
| 1 | Financial-Models-Numerical-Methods | 5,258 |
| 2 | DifferentialEquations.jl | 2,756 |
| 3 | neuraloperator | 1,776 |
| 4 | NeuralPDE.jl | 903 |
| 5 | DiffEqFlux.jl | 837 |
| 6 | SciMLTutorials.jl | 708 |
| 7 | FreeFem-sources | 702 |
| 8 | dolfinx | 656 |
| 9 | Gridap.jl | 640 |
| 10 | PDEBench | 618 |
| 11 | ApproxFun.jl | 524 |
| 12 | 18S096SciML | 303 |
| 13 | DiffEqBase.jl | 297 |
| 14 | SciMLBenchmarks.jl | 290 |
| 15 | FourierFlows.jl | 197 |
| 16 | p4pdes | 178 |
| 17 | pyclaw | 150 |
| 18 | MethodOfLines.jl | 148 |
| 19 | QuantPDE | 54 |
| 20 | rodin | 34 |
| 21 | nvidia-modulus-airfoil-optimisation | 21 |
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