Accelerating a hybrid continuum-atomistic fluidic model with on-the-fly machine learning

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.