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Spatio-temporal systems exhibiting multi-scale behaviour are common inapplications ranging from cyber-physical systems to systems biology, yet theypresent formidable challenges for computational modelling and analysis. Here weconsider a prototypic scenario where spatially distributed agents decide theirmovement based on external inputs and a fast-equilibrating internalcomputation. We propose a generally applicable strategy based on statisticallyabstracting the internal system using Gaussian Processes, a powerful class ofnon-parametric regression techniques from Bayesian Machine Learning. We show ona running example of bacterial chemotaxis that this approach leads to accurateand much faster simulations in a variety of scenarios.

Statistical abstraction for multi-scale spatio-temporal systems