  Long-period circumbinary planets appear to be as common as those orbiting
single stars and have been found to frequently have orbital radii just beyond
the critical distance for dynamical stability. Assessing the stability is
typically done either through N-body simulations or using the stability
criterion first considered by Dvorak and later developed by Holman and Wiegert:
a second-order polynomial calibrated to broadly match numerical simulations.
However, the polynomial is unable to capture islands of instability introduced
by mean motion resonances, causing the accuracy of the criterion to approach
that of a random coin-toss when close to the boundary. We show how a deep
neural network (DNN) trained on N-body simulations generated with REBOUND is
able to significantly improve stability predictions for circumbinary planets on
initially coplanar, circular orbits. Specifically, we find that the accuracy of
our DNN never drops below 86%, even when tightly surrounding the boundary of
instability, and is fast enough to be practical for on-the-fly calls during
likelihood evaluations typical of modern Bayesian inference. Our binary
classifier DNN is made publicly available at
https://github.com/CoolWorlds/orbital-stability
