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Quantization applied to the visualization of low-probability flooding events

Abstract : Visualization is essential in the risk assessment of coastal or river flooding. In this work, we deal with expensive-to-evaluate hydraulic simulators, taking as random scalar inputs offshore meteo-oceanic conditions and dyke breach parameters, whereas the output is a flooding map. The challenge is to display a few prototype maps representing at best the probability law of the flooding event, which is a typical quantization problem. The K-Means algorithm classically serves to minimize the expected squared distance between samples of the random event and their representatives [1]. This clustering technique is adapted to handle three key specificities of our context. First, the quantization is done in the specific space of flooding maps, which requires to define an appropriate distance measure, such as a weighted L2 distance in a matrix space. Second, because of the timeconsuming simulators, the clustering is done in a space defined by Gaussian process proxies of the maps [2]. Third, flooding being a low-probability event, traditional Monte Carlo approaches are inefficient and an Importance Sampling scheme is introduced to generate the maps. The prototype maps obtained represent the distribution of the floodings and each is associated to a probability mass. To discriminate between the scenarii leading to similar flooding events, a second quantization procedure is carried out in the input space within each cluster. The method is evaluated on an analytical example before being extended to the coastal case of Les Boucholeurs on the French Atlantic coast [3].
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https://hal-emse.ccsd.cnrs.fr/emse-03720115
Contributor : Florent Breuil Connect in order to contact the contributor
Submitted on : Wednesday, July 20, 2022 - 3:04:13 PM
Last modification on : Tuesday, November 15, 2022 - 10:58:34 AM

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  • HAL Id : emse-03720115, version 1

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Charlie Sire, Rodolphe Le Riche, Didier Rullière, Jérémy Rohmer, Lucie Pheulpin, et al.. Quantization applied to the visualization of low-probability flooding events. The 8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2022), Jun 2022, Oslo, Norway. ⟨emse-03720115⟩

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