# Statistical abstraction for multi-scale spatio-temporal systems

## TL;DR

This paper introduces a Gaussian Process-based statistical abstraction method to efficiently simulate multi-scale spatio-temporal systems, demonstrated on bacterial chemotaxis.

## Contribution

It presents a novel approach using Gaussian Processes to abstract internal dynamics, enabling faster and accurate simulations of complex multi-scale systems.

## Key findings

- Gaussian Process abstraction improves simulation speed
- Method achieves high accuracy in bacterial chemotaxis modeling
- Applicable to various multi-scale spatio-temporal systems

## Abstract

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.