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Toward efficient parameter sweeping and optimisation of fluid performance models by Taylor-model based symbolic numerical integration

Richard Hayden

National Workshop Paper
10th Workshop on Process Algebra and Stochastically Timed Activities (PASTA 2011)
September, 2011

Fluid-approximation or mean-field techniques are currently very popular approaches to the efficient analysis of massively-parallel Markov models. In this paper, we exploit the ODE-representation of these approximations to develop efficient techniques for simultaneous partially-symbolic numerical integration over parameter ranges. In particular, we borrow the Taylor model data structure of Makino and Berz [14] from the field of verified numerical integration. We use this to compute, in an efficient manner, tight bounds on the range of the ODE solutions over time with parameters lying in large intervals. This has applications to fast parameter sweeping, sensitivity analysis and global optimisation of model parameters in performance models amenable to fluid approximation.

[14] K. Makino and M. Berz. Remainder Differential Algebras and Their Applications. In Computational Differentiation: Techniques, Applications, and Tools, pages 63-74. SIAM, 1996.

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