  We formulate the predicted-updates dynamic model, one of the first
beyond-worst-case models for dynamic algorithms, which generalizes a large set
of well-studied dynamic models including the offline dynamic, incremental, and
decremental models to the fully dynamic setting when given predictions about
the update times of the elements. In the most basic form of our model, we
receive a set of predicted update times for all of the updates that occur over
the event horizon. We give a novel framework that "lifts" offline
divide-and-conquer algorithms into the fully dynamic setting with little
overhead. Using this, we are able to interpolate between the offline and fully
dynamic settings; when the $\ell_1$ error of the prediction is linear in the
number of updates, we achieve the offline runtime of the algorithm (up to
$\mathrm{poly} \log n$ factors). Provided a fully dynamic backstop algorithm,
our algorithm will never do worse than the backstop algorithm regardless of the
prediction error. Furthermore, our framework achieves a smooth linear trade-off
between $\ell_1$ error in the predictions and runtime. These correspond to the
desiderata of consistency, robustness, and graceful degradation of the
algorithms-with-predictions literature. We further extend our techniques to
incremental and decremental settings, transforming algorithms in these settings
when given predictions of only the deletion and insertion times, respectively.
Our framework is general, and we apply it to obtain improved efficiency bounds
over the state-of-the-art dynamic algorithms for a variety of problems
including triconnectivity, planar digraph all pairs shortest paths, $k$-edge
connectivity, and others, for prediction error of reasonable magnitude.
