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arXiv:1704.07715astro-ph.IM

JANUS: A bit-wise reversible integrator for N-body dynamics

Hanno Rein, Daniel Tamayo

Abstract

Hamiltonian systems such as the gravitational N-body problem have time-reversal symmetry. However, all numerical N-body integration schemes, including symplectic ones, respect this property only approximately. In this paper, we present the new N-body integrator JANUS, for which we achieve exact time-reversal symmetry by combining integer and floating point arithmetic. JANUS is explicit, formally symplectic and satisfies Liouville's theorem exactly. Its order is even and can be adjusted between two and ten. We discuss the implementation ofJANUS and present tests of its accuracy and speed by performing and analyzing long-term integrations of the Solar System. We show that JANUS is fast and accurate enough to tackle a broad class of dynamical problems. We also discuss the practical and philosophical implications of running exactly time-reversible simulations.

arXiv comments
Accepted for publication by MNRAS, 7 pages, 4 figures, source code available at https://github.com/hannorein/rebound , iPython notebooks to reproduce figures available at https://github.com/hannorein/JanusPaper
Journal reference
DOI
doi:10.1093/mnras/stx2479
Subjects
astro-ph.IMInstrumentation and Methods for Astrophysics astro-ph.COCosmology and Nongalactic Astrophysics astro-ph.EPEarth and Planetary Astrophysics

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Discussed in comments3 threads

  1. How can AI researchers save energy? By going backward 1 comment

    • I'm sceptical about the energy motivation, but there are multiple reasons why making invertible deep learning architectures can be interesting or useful. Cf, a series of workshops from 2019-2021: https://invertibleworkshop.github.io/ Since then diffusion models have been…

      imurrayView on HNParent context

  2. The random walk of cars and their collision probabilities with planets 1 comment

    • Hanno Rein and Daniel Tamayo are pretty legit dynamicists. For anyone interested in doing calculations like these themselves, they've been working on this amazing N-body library called Rebound: https://github.com/hannorein/rebound One of my all-time favorite figures is Fig. 1 of…

      antogniniView on HNParent context

  3. Over 150 new families of Newtonian periodic planar three-body orbits 1 comment

    • Hanno Rein, one of the experts in the field, just published a new algorithm which is exactly time-reversible for floating point numbers. Figure 1 of the paper is pretty incredible: https://arxiv.org/abs/1704.07715

      antogniniView on HNParent context

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