Design and analysis of multi-level numerical experiments, with application to fire safety

Rémi Stroh (1, 2, 3) , Julien Bect (2, 3) , Séverine Demeyer (1) , Nicolas Fischer (1) , Emmanuel Vazquez (2, 3)

1 LNE - Laboratoire National de Métrologie et d'Essais [Trappes]
2 L2S - Laboratoire des signaux et systèmes
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

To assess the conformity of a building in case of fire, fire engineers use numerical simulations. A popular software for fire simulations is Fire Dynamics Simulator (FDS). It is based on a finite difference method that takes into account the random behavior of the fire. Thus, the response of FDS is stochastic. The mesh size used in the numerical scheme can be chosen by the user. When the mesh size decreases, the accuracy and the computation time of simulations increase. At low accuracy, one simulation takes a few minutes to run, whereas it can be several weeks at high accuracy. We consider the problem of estimating the behavior of fine-mesh simulations (high-fidelity), using a combination of fine-and coarse-mesh simulations (low-fidelity). This approach is called multi-fidelity. We propose to extend the Bayesian multi-fidelity models proposed by Picheny and Ginsbourger (SIAM/ASA Journal on Uncertainty Quantification, 1(1):57-78, 2013) and Tuo et al. (Technometrics, 56(3):372-380, 2014) to the case of stochastic simulators.

Domaines: Calcul [stat.CO]

Rémi Stroh, Julien Bect, Séverine Demeyer, Nicolas Fischer, Emmanuel Vazquez. Design and analysis of multi-level numerical experiments, with application to fire safety. Journées annuelles du GdR MASCOT NUM (MASCOT NUM 2016), Mar 2016, Toulouse, France. ⟨hal-01331171⟩