Location Aggregation of Spatial Population CTMC Models

TL;DR

This paper introduces a heuristic method combining stochastic approximation and spectral clustering to aggregate spatial locations in CTMC models, reducing computational costs while maintaining dynamical accuracy.

Contribution

It presents a novel aggregation approach for spatial CTMC models that balances efficiency and accuracy, validated on epidemic and bike sharing case studies.

Findings

Aggregation reduces computational cost significantly.

Method maintains key dynamical behaviors.

Effective on epidemic and bike sharing models.

Abstract

In this paper we focus on spatial Markov population models, describing the stochastic evolution of populations of agents, explicitly modelling their spatial distribution, representing space as a discrete, finite graph. More specifically, we present a heuristic approach to aggregating spatial locations, which is designed to preserve the dynamical behaviour of the model whilst reducing the computational cost of analysis. Our approach combines stochastic approximation ideas (moment closure, linear noise), with computational statistics (spectral clustering) to obtain an efficient aggregation, which is experimentally shown to be reasonably accurate on two case studies: an instance of epidemic spreading and a London bike sharing scenario.