  We present a hybrid continuum-atomistic scheme which combines molecular
dynamics (MD) simulations with on-the-fly machine learning techniques for the
accurate and efficient prediction of multiscale fluidic systems. By using a
Gaussian process as a surrogate model for the computationally expensive MD
simulations, we use Bayesian inference to predict the system behaviour at the
atomistic scale, purely by consideration of the macroscopic inputs and outputs.
Whenever the uncertainty of this prediction is greater than a predetermined
acceptable threshold, a new MD simulation is performed to continually augment
the database, which is never required to be complete. This provides a
substantial enhancement to the current generation of hybrid methods, which
often require many similar atomistic simulations to be performed, discarding
information after it is used once.
  We apply our hybrid scheme to nano-confined unsteady flow through a
high-aspect-ratio converging-diverging channel, and make comparisons between
the new scheme and full MD simulations for a range of uncertainty thresholds
and initial databases. For low thresholds, our hybrid solution is highly
accurate\,---\,within the thermal noise of a full MD simulation. As the
uncertainty threshold is raised, the accuracy of our scheme decreases and the
computational speed-up increases (relative to a full MD simulation), enabling
the compromise between precision and efficiency to be tuned. The speed-up of
our hybrid solution ranges from an order of magnitude, with no initial
database, to cases where an extensive initial database ensures no new MD
simulations are required.
