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.
M. Michaelides and G. Sanguinetti are supported by the European Research Council under grant MLCS 306999. J. Hillston is supported by the EU project, QUANTICOL 600708.
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- 1.
The pCTMC is the internal model for a single agent here, not for multiple agents.
- 2.
It is highly unlikely to have more than a single transition since (m, L) are continuous values that constantly change for the bacterium.
- 3.
We sub-sample because the KS test p-value depends heavily on sample size. Even if two distributions generating samples might be very close, in the limit of an infinite sample size one approaches the true distributions. In such a case, the KS test will reject that the two samples were produced by the same distribution, returning lower p-values as sample size increases (for the same KS distance). We do not expect to produce the same distributions here since we are making approximations, so comparing p-values for very large sample sizes is not of interest.
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Michaelides, M., Hillston, J., Sanguinetti, G. (2017). Statistical Abstraction for Multi-scale Spatio-Temporal Systems. In: Bertrand, N., Bortolussi, L. (eds) Quantitative Evaluation of Systems. QEST 2017. Lecture Notes in Computer Science(), vol 10503. Springer, Cham. https://doi.org/10.1007/978-3-319-66335-7_15
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