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Space filling designs for computer experiments: some algorithms and numerical results on industrial problems

Presented by: 
B Iooss [EDF R&D]
Tuesday 6th September 2011 - 10:00 to 10:30
INI Seminar Room 1
Session Title: 
Design I
Session Chair: 
P. Challoner
Complex computer codes, for instance simulating physical phenomena, are often too time expensive to be directly used to perform uncertainty, sensitivity, optimization and robustness analyses. A widely accepted method to circumvent this problem consists in replacing cpu time expensive computer models by cpu inexpensive mathematical functions, called metamodels. A necessary condition to a successful modelling of these computer experiments is to explore the whole space of variations of the computer model input variables. However in many industrial applications, we are faced to the harsh problem of the high dimensionality of the exploration space. In this communication, we will first focus on the metamodel validation process which consists in evaluating the metamodel predictivity with respect to the initial computer code. This step has to be realized with caution and robustness in industrial applications, especially in the framework of safety studies.

We propose and test an algorithm, which optimizes the distance between the validation points and the metamodel learning points in order to estimate the true metamodel predictivity with a minimum number of validation points. Comparisons with classical validation algorithms and application to a nuclear safety computer code show the relevance of this sequential validation design. Second, we will present some recent results about the properties of different space filling designs. In practice, one has to choose which design to use in an exploratory phase of a numerical model. We will show the usefulness of some classification tools, as those based on the minimal spanning trees. We adopt a numerical approach to compare the performance of different types of space filling designs, in function of their interpoint-distance, L2-discrepancies and various sub-projection properties. Finally, we will present two recent problems, posed in some industrial applications: the introductions of inequality constraints between the inputs of a space filling design and the building of space filling design mixing quantitative and qualitative factors.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons