  Large-scale numerical simulations are used across many scientific disciplines
to facilitate experimental development and provide insights into underlying
physical processes, but they come with a significant computational cost. Deep
neural networks (DNNs) can serve as highly-accurate surrogate models, with the
capacity to handle diverse datatypes, offering tremendous speed-ups for
prediction and many other downstream tasks. An important use-case for these
surrogates is the comparison between simulations and experiments; prediction
uncertainty estimates are crucial for making such comparisons meaningful, yet
standard DNNs do not provide them. In this work we define the fundamental
requirements for a DNN to be useful for scientific applications, and
demonstrate a general variational inference approach to equip predictions of
scalar and image data from a DNN surrogate model trained on inertial
confinement fusion simulations with calibrated Bayesian uncertainties.
Critically, these uncertainties are interpretable, meaningful and preserve
physics-correlations in the predicted quantities.
