Prédiction d'images par krigeage et ACP sur base d'ondelettes, avec application à un modèle d'inondation côtière

Abstract : This research is motivated by the study of coastal flooding with a time-consuming numerical simulator. Each simulator run provides an image, corresponding to a map of flooded water level, depending on input parameters linked to the sea. The aim is to predict an image for a new set of input values. In this framework, a standard approach consists of 1) To reduce dimension of the image, viewed as a vector of pixels, by principal component analysis (PCA); 2) To build a Gaussian process regression model-or Kriging model-on the first principal components; 3) To predict with this model. However, step 1) is hardly applicable for a large number of pixels. Furthermore, it does not account for the spatial regularity of the image. To address these issues, we propose to modify step 1) by doing a functional PCA based on wavelets on the image, now viewed as a function. We show how to select a unique number of wavelets, common to all images of the learning set, in order to guarantee a sufficient approximation quality. The methodology is applied to the coastal flooding model on images with 4096 pixels. Predictions are 5 times faster as for standard PCA, for at least equivalent predictive performances.
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https://hal.archives-ouvertes.fr/hal-02144126
Contributor : Tran Vi-Vi Élodie Perrin <>
Submitted on : Wednesday, May 29, 2019 - 6:54:20 PM
Last modification on : Saturday, June 8, 2019 - 1:17:16 AM

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Tran Vi-Vi Élodie Perrin, Olivier Roustant, Jérémy Rohmer, Olivier Alata. Prédiction d'images par krigeage et ACP sur base d'ondelettes, avec application à un modèle d'inondation côtière. 2019. ⟨hal-02144126⟩

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