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}
}Via pip:
$ pip install heyokaVia conda + conda-forge:
$ conda install heyoka.pyThe full documentation can be found here.
- Francesco Biscani (European Space Agency)
- Dario Izzo (European Space Agency)
heyoka.py is released under the MPL-2.0 license.
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