  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.
