A Bayesian neural network predicts the dissolution of compact planetary systems
arXiv:2101.04117 · doi:10.1073/pnas.2026053118
Abstract
Despite over three hundred years 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 novel internal structure inspired from dynamics theory. Our Bayesian neural network model 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 N-body 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 near-resonant three-planet configurations, the model demonstrates robust generalization to both non-resonant and higher multiplicity configurations, in the latter case outperforming models fit to that specific set of integrations. The model computes instability estimates up to five orders of magnitude faster than a numerical integrator, and unlike previous efforts provides confidence intervals on its predictions. Our inference model is publicly available in the SPOCK package, with training code open-sourced.
arXiv comment8 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
References in corpus (37)
- XGBoost: A Scalable Tree Boosting System
- SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
- Array Programming with NumPy
- PyTorch: An Imperative Style, High-Performance Deep Learning Library
- Sequence to Sequence Learning with Neural Networks
- Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning
- REBOUND: An open-source multi-purpose N-body code for collisional dynamics
- WHFast: A fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long term gravitational simulations
- The California-Kepler Survey V. Peas in a Pod: Planets in a Kepler Multi-planet System are Similar in Size and Regularly Spaced
- Discovering Symbolic Models from Deep Learning with Inductive Biases
- Fast Automated Analysis of Strong Gravitational Lenses with Convolutional Neural Networks
- Multiplicative Normalizing Flows for Variational Bayesian Neural Networks
- Deep learning of multi-element abundances from high-resolution spectroscopic data
- First order resonance overlap and the stability of close two planet systems
- Post-Oligarchic Evolution of Protoplanetary Embryos and the Stability of Planetary Systems
- Bayesian Deep Learning and a Probabilistic Perspective of Generalization
- Uncertainties in Parameters Estimated with Neural Networks: Application to Strong Gravitational Lensing
- Three Body Resonance Overlap in Closely Spaced Multiple Planet Systems
- Predicting the long-term stability of compact multiplanet systems
- Convergent Migration Renders TRAPPIST-1 Long-lived
- Stochastic Gradient Descent as Approximate Bayesian Inference
- The stability of tightly-packed, evenly-spaced systems of Earth-mass planets orbiting a Sun-like star
- The Orbital Stability of Planets Trapped in the First-Order Mean-Motion Resonances
- A Criterion for the Onset of Chaos in Systems of Two Eccentric Planets
- The statistical mechanics of planet orbits
- Bayesian Layers: A Module for Neural Network Uncertainty
- A Machine Learns to Predict the Stability of Tightly Packed Planetary Systems
- The path to instability in compact multi-planetary systems
- Hill stability in the AMD framework
- Dynamics and Accretion of Planetesimals
- An Integrable Model for the Dynamics of Planetary Mean Motion Resonances
- Survival of non-coplanar, closely-packed planetary systems after a close encounter
- Dynamical instability and its implications for planetary system architecture
- Fundamental limits from chaos on instability time predictions in compact planetary systems
- Stability Constrained Characterization of Multiplanet Systems
- Nekhoroshev Estimates for the Survival Time of Tightly Packed Planetary Systems
- Is SGD a Bayesian sampler? Well, almost