# A Bayesian neural network predicts the dissolution of compact planetary systems

@article{Cranmer2021ABN, title={A Bayesian neural network predicts the dissolution of compact planetary systems}, author={M. Cranmer and Daniel Tamayo and Hanno Rein and Peter W. Battaglia and Sam Hadden and Philip J. Armitage and Shirley Ho and David N. Spergel}, journal={Proceedings of the National Academy of Sciences of the United States of America}, year={2021}, volume={118} }

Significance Despite over 300 y of effort, no solutions exist for predicting when a general planetary configuration will become unstable. We introduce a deep learning architecture to push forward this problem for compact systems. While current machine learning algorithms in this area rely on scientist-derived instability metrics, our new technique learns its own metrics from scratch, enabled by a internal structure inspired from dynamics theory. Our model can quickly and accurately predictβ¦Β

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## References

SHOWING 1-10 OF 98 REFERENCES

A Machine Learns to Predict the Stability of Tightly Packed Planetary Systems

- Physics, Geology
- 2016

It is found that training an XGBoost machine learning algorithm on physically motivated features yields an accurate classifier of stability in packed systems, and motivates investing computational resources to train algorithms capable of predicting stability over longer timescales and over broader regions of phase space.

Predicting the long-term stability of compact multiplanet systems

- Geology, PhysicsProceedings of the National Academy of Sciences
- 2020

The Stability of Planetary Orbital Configurations Klassifier (SPOCK) predicts stability using physically motivated summary statistics measured in integrations of the first 104 orbits, thus achieving speed-ups of up to 105 over full simulations, which computationally opens up the stability-constrained characterization of multiplanet systems.

Fundamental limits from chaos on instability time predictions in compact planetary systems

- Physics, Geology
- 2019

Instabilities in compact planetary systems are generically driven by chaotic dynamics. This implies that an instability time measured through direct N-body integration is not exact, but ratherβ¦

Dynamical instability and its implications for planetary system architecture

- Physics, GeologyMonthly Notices of the Royal Astronomical Society
- 2019

We examine the effects that dynamical instability has on shaping the orbital properties of exoplanetary systems. Using N-body simulations of non-EMS (Equal Mutual Separation), multi-planet systems weβ¦

Nekhoroshev Estimates for the Survival Time of Tightly Packed Planetary Systems

- Physics, GeologyThe Astrophysical Journal
- 2020

$N$-body simulations of non-resonant tightly-packed planetary systems have found that their survival time (i.e. time to first close encounter) grows exponentially with their interplanetary spacingβ¦

Bayesian Deep Learning and a Probabilistic Perspective of Generalization

- Computer ScienceNeurIPS
- 2020

It is shown that deep ensembles provide an effective mechanism for approximate Bayesian marginalization, and a related approach is proposed that further improves the predictive distribution by marginalizing within basins of attraction, without significant overhead.

Deep learning of multi-element abundances from high-resolution spectroscopic data

- Computer Science, PhysicsMonthly Notices of the Royal Astronomical Society
- 2018

This work designs a neural network for high-resolution spectroscopic analysis using APOGEE data that mimics the methodology of standard spectroscopy analyses: stellar parameters are determined using the full wavelength range, but individual element abundances use censored portions of the spectrum.

THE STATISTICAL MECHANICS OF PLANET ORBITS

- Physics, Geology
- 2015

The final ?giant-impact? phase of terrestrial planet formation is believed to begin with a large number of planetary ?embryos? on nearly circular, coplanar orbits. Mutual gravitational interactionsβ¦

The Stability of Multi-Planet Systems

- Physics, Geology
- 1996

A system of two small planets orbiting the Sun on low-eccentricity, low-inclination orbits is stable with respect to close encounters if the initial semi-major axis difference, Ξ, measured in mutualβ¦

Hill stability in the AMD framework

- Physics, GeologyAstronomy & Astrophysics
- 2018

In a two-planet system, a topological boundary that is created by Sundman (1912, Acta Math., 36, 105) inequality can forbid close encounters between the two planets for an infinite time. A system isβ¦