A Bayesian neural network predicts the dissolution of compact planetary systems
Abstract
We introduce a Bayesian neural network model that can accurately predict not only if, but also when a compact planetary system with three or more planets will go unstable. Our model, trained directly from short Nbody time series of raw orbital elements, is more than two orders of magnitude more accurate at predicting instability times than analytical estimators, while also reducing the bias of existing machine learning algorithms by nearly a factor of three. Despite being trained on compact resonant and nearresonant threeplanet configurations, the model demonstrates robust generalization to both nonresonant and higher multiplicity configurations, in the latter case outperforming models fit to that specific set of integrations. The model computes instability estimates up to <math xmlns="http://www.w3.org/1998/Math/MathML" id="i1" overflow="scroll"><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mn>5</mn></mrow></msup></math> times faster than a numerical integrator, and unlike previous efforts provides confidence intervals on its predictions. Our inference model is publicly available in the SPOCK (https://github.com/dtamayo/spock) package, with training code open sourced (https://github.com/MilesCranmer/bnn_chaos_model).
 Publication:

Proceedings of the National Academy of Science
 Pub Date:
 October 2021
 DOI:
 10.1073/pnas.2026053118
 arXiv:
 arXiv:2101.04117
 Bibcode:
 2021PNAS..11826053C
 Keywords:

 deep learning;
 UAT:2173;
 Bayesian analysis;
 chaos;
 Astrophysics  Earth and Planetary Astrophysics;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 Computer Science  Artificial Intelligence;
 Computer Science  Machine Learning;
 Statistics  Machine Learning
 EPrint:
 8 content pages, 7 appendix and references. 8 figures. Source code at: https://github.com/MilesCranmer/bnn_chaos_model inference code at https://github.com/dtamayo/spock