heyoka.py

Modern Taylor's method via just-in-time compilation
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The heyókȟa [...] is a kind of sacred clown in the culture of the Sioux (Lakota and Dakota people) of the Great Plains of North America. The heyoka is a contrarian, jester, and satirist, who speaks, moves and reacts in an opposite fashion to the people around them.

heyoka.py is a Python library for the integration of ordinary differential equations (ODEs) via Taylor's method, based on automatic differentiation techniques and aggressive just-in-time compilation via LLVM. Notable features include:

• support for single-precision, double-precision, extended-precision (80-bit and 128-bit), and arbitrary-precision floating-point types,
• high-precision zero-cost dense output,
• accurate and reliable event detection,
• builtin support for analytical mechanics - bring your own Lagrangians/Hamiltonians and let heyoka.py formulate and solve the equations of motion,
• builtin support for high-order variational equations - compute not only the solution, but also its partial derivatives,
• builtin support for machine learning applications via neural network models,
• the ability to maintain machine precision accuracy over tens of billions of timesteps,
• batch mode integration to harness the power of modern SIMD instruction sets (including AVX/AVX2/AVX-512/Neon/VSX),
• ensemble simulations and automatic parallelisation,
• interoperability with SymPy.

heyoka.py is based on the heyoka C++ library.

If you are using heyoka.py as part of your research, teaching, or other activities, we would be grateful if you could star the repository and/or cite our work. For citation purposes, you can use the following BibTex entry, which refers to the heyoka.py paper (arXiv preprint):

@article{10.1093/mnras/stab1032,
    author = {Biscani, Francesco and Izzo, Dario},
    title = "{Revisiting high-order Taylor methods for astrodynamics and celestial mechanics}",
    journal = {Monthly Notices of the Royal Astronomical Society},
    volume = {504},
    number = {2},
    pages = {2614-2628},
    year = {2021},
    month = {04},
    issn = {0035-8711},
    doi = {10.1093/mnras/stab1032},
    url = {https://doi.org/10.1093/mnras/stab1032},
    eprint = {https://academic.oup.com/mnras/article-pdf/504/2/2614/37750349/stab1032.pdf}
}

heyoka.py's novel event detection system is described in the following paper (arXiv preprint):

@article{10.1093/mnras/stac1092,
    author = {Biscani, Francesco and Izzo, Dario},
    title = "{Reliable event detection for Taylor methods in astrodynamics}",
    journal = {Monthly Notices of the Royal Astronomical Society},
    volume = {513},
    number = {4},
    pages = {4833-4844},
    year = {2022},
    month = {04},
    issn = {0035-8711},
    doi = {10.1093/mnras/stac1092},
    url = {https://doi.org/10.1093/mnras/stac1092},
    eprint = {https://academic.oup.com/mnras/article-pdf/513/4/4833/43796551/stac1092.pdf}
}

Installation

Via pip:

$ pip install heyoka

Via conda + conda-forge:

$ conda install heyoka.py

Documentation

The full documentation can be found here.

Authors

• Francesco Biscani (European Space Agency)
• Dario Izzo (European Space Agency)

License

heyoka.py is released under the MPL-2.0 license.