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Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R
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# SciMLBenchmarks.jl: Benchmarks for Scientific Machine Learning (SciML) and Equation Solvers
[](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)
[](https://docs.sciml.ai/SciMLBenchmarksOutput/stable/)
[](https://github.com/SciML/SciMLBenchmarks.jl/actions/workflows/benchmarks.yml)
[](https://github.com/SciML/ColPrac)
[](https://github.com/SciML/SciMLStyle)
SciMLBenchmarks.jl holds webpages, pdfs, and notebooks showing the benchmarks
for the SciML Scientific Machine Learning Software ecosystem, including:
- Benchmarks of equation solver implementations
- Speed and robustness comparisons of methods for parameter estimation / inverse problems
- Training universal differential equations (and subsets like neural ODEs)
- Training of physics-informed neural networks (PINNs)
- Surrogate comparisons, including radial basis functions, neural operators (DeepONets, Fourier Neural Operators), and more
The SciML Bench suite is made to be a comprehensive open source benchmark from the ground up, covering the methods of
computational science and scientific computing all the way to AI for science.
## Rules: Optimal, Fair, and Reproducible
These benchmarks are meant to represent good optimized coding style. Benchmarks are preferred to be run on the provided open
benchmarking hardware for full reproducibility (though in some cases, such as with language barriers, this can be difficult).
Each benchmark is documented with the compute devices used along with package versions for necessary reproduction. These
benchmarks attempt to measure in terms of work-precision efficiency, either timing with approximately matching error
or building work-precision diagrams for direct comparison of speed at given error tolerances.
**If any of the code from any of the languages can be improved, please open a pull request**.
For critiques of benchmarks, please open a pull request that changes the code in the desired manner. Issues with recommended
changes are generally vague and not actionable, while pull requests with code changes are exact. Thus if there is something
you think should be changed in the code, please make the recommended change in the code!
## Results
To view the results of the SciML Benchmarks, go to [docs.sciml.ai/SciMLBenchmarksOutput](https://docs.sciml.ai/SciMLBenchmarksOutput/stable/). By default, this
will lead to the latest tagged version of the benchmarks. To see the in-development version of the benchmarks, go to
[https://docs.sciml.ai/SciMLBenchmarksOutput/dev/](https://docs.sciml.ai/SciMLBenchmarksOutput/dev/).
Static outputs in pdf, markdown, and html reside in [SciMLBenchmarksOutput](https://github.com/SciML/SciMLBenchmarksOutput).
## Citing
To cite the SciML Benchmarks, please cite the following:
```bib
@article{rackauckas2019confederated,
title={Confederated modular differential equation APIs for accelerated algorithm development and benchmarking},
author={Rackauckas, Christopher and Nie, Qing},
journal={Advances in Engineering Software},
volume={132},
pages={1--6},
year={2019},
publisher={Elsevier}
}
@article{DifferentialEquations.jl-2017,
author = {Rackauckas, Christopher and Nie, Qing},
doi = {10.5334/jors.151},
journal = {The Journal of Open Research Software},
keywords = {Applied Mathematics},
note = {Exported from https://app.dimensions.ai on 2019/05/05},
number = {1},
pages = {},
title = {DifferenExcerpt of 17,493 characters
Read on GitHubWould you bet a product on this? Bounded 0–100 and slow moving.
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