Nouvian, Morgane

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Data-Informed Parameter Synthesis for Population Markov Chains

2019-09-17, Hajnal, Matej, Nouvian, Morgane, Petrov, Tatjana, Safranek, David

Population models are widely used to model different phenomena: animal collectives such as social insects, flocking birds, schooling fish, or humans within societies, as well as molecular species inside a cell, cells forming a tissue. Animal collectives show remarkable self-organisation towards emergent behaviours without centralised control. Quantitative models of the underlying mechanisms can directly serve important societal concerns (for example, prediction of seismic activity [5]), inspire the design of distributed algorithms (for example, ant colony algorithm [1]), or aid robust design and engineering of collective, adaptive systems under given functionality and resources, which is recently gaining attention in vision of smart cities [3, 4]. Quantitative prediction of the behaviour of a population of agents over time and space, each having several behavioural modes, results in a high-dimensional, non-linear, and stochastic system [2]. Hence, computational modelling with population models is challenging, especially when the model parameters are unknown and experiments are expensive.

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Data-Informed Parameter Synthesis for Population Markov Chains

2019-08-01, Hajnal, Matej, Nouvian, Morgane, Safranek, David, Petrov, Tatjana

Stochastic population models are widely used to model phenomena in different areas such as chemical kinetics or collective animal behaviour. Quantitative analysis of stochastic population models easily becomes challenging, due to the combinatorial propagation of dependencies across the population. The complexity becomes especially prominent when model’s parameters are not known and available measurements are limited. In this paper, we illustrate this challenge in a concrete scenario: we assume a simple communication scheme among identical individuals, inspired by how social honeybees emit the alarm pheromone to protect the colony in case of danger. Together, n individuals induce a population Markov chain with n parameters. In addition, we assume to be able to experimentally observe the states only after the steady-state is reached. In order to obtain the parameters of the individual’s behaviour, by utilising the data measurements for population, we combine two existing techniques. First, we use the tools for parameter synthesis for Markov chains with respect to temporal logic properties, and then we employ CEGAR-like reasoning to find the viable parameter space up to desired coverage. We report the performance on a number of synthetic data sets.