  Spatio-temporal systems exhibiting multi-scale behaviour are common in
applications ranging from cyber-physical systems to systems biology, yet they
present formidable challenges for computational modelling and analysis. Here we
consider a prototypic scenario where spatially distributed agents decide their
movement based on external inputs and a fast-equilibrating internal
computation. We propose a generally applicable strategy based on statistically
abstracting the internal system using Gaussian Processes, a powerful class of
non-parametric regression techniques from Bayesian Machine Learning. We show on
a running example of bacterial chemotaxis that this approach leads to accurate
and much faster simulations in a variety of scenarios.
