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Functional-input metamodeling: an application to coastal flood early warning

Abstract : Currently, floods in general affect more people than any other hazard. In just the last decade of the 20th century, more than 1.5 billion were affected. In the seek to mitigate the impact of this type of hazard, strong scientific effort has been devoted to the constitution of computer codes that could be used as risk management tools. Available computer models now allow properly modelling coastal flooding events at a fairly high resolution. Unfortunately,their use is strongly prohibitive for early warning, with a simulation of few hours of maritime dynamics taking several hours to days of processing time, even on multi-processor clusters.This thesis is part of the ANR RISCOPE project, which aims at addressing this limitation by means of surrogate modeling of the hydrodynamic computer codes.As a particular requirement of this application, the metamodel should be able to deal with functional inputs corresponding to time varying maritime conditions. To this end, we focused on Gaussian process metamodels, originally developed for scalar inputs, but now available also for functional inputs. The nature of the inputs gave rise to a number of questions about the proper way to represent them in the metamodel: (i) which functional inputs are worth keeping as predictors, (ii) which dimension reduction method (e.g., B-splines, PCA, PLS) is ideal, (iii) which is a suitable projection dimension, and given our choice to work with Gaussian process metamodels, also the question of (iv) which is a convenient distance to measure similarities between functional input points within the kernel function. Some ofthese characteristics - hereon called structural parameters - of the model and some others such as the family of kernel (e.g., Gaussian, Matérn 5/2) are often arbitrarily chosen a priori.Sometimes, those are selected based on other studies. As one may intuit and has been shown by us through experiments, those decisions could have a strong impact on the prediction capability of the resulting model. Thus, without losing sight of our final goal of contributing to the improvement of coastal flooding early warning, we undertook the construction of an efficient methodology to set up the structural parameters of the model. As a first solution, we proposed an exploration approach based on the Response Surface Methodology. It was effectively used to tune the metamodel for an analytic toy function,as well as for a simplified version of the code studied in RISCOPE. While relatively simple,the proposed methodology was able to find metamodel configurations of high prediction capability with savings of up to 76.7% and 38.7% of the time spent by an exhaustive search approach in the analytic case and coastal flooding case, respectively. The solution found by our methodology was optimal in most cases. We developed later a second prototype based on Ant Colony Optimization (ACO). This new approach is more powerful in terms of solution time and flexibility in the features of the model allowed to be explored. The ACO based method smartly samples the solution space and progressively converges towards the optimal configuration. The collection of statistical tools used for metamodeling in this thesis motivated the development of the fun Gp R package, which is now available in GitHub and about to be submitted to CRAN. In an independent work, we studied the estimation of the covariance parameters of a Transformed Gaussian Process by Maximum Likelihood (ML) and Cross Validation. We showed that both estimators are consistent and asymptotically normal. In the case of ML,these results can be interpreted as a proof of robustness of Gaussian ML in the case of non-Gaussian processes.
Keywords : Metamodeling
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José Betancourt. Functional-input metamodeling: an application to coastal flood early warning. Statistics [math.ST]. Université Toulouse 3 - Paul Sabatier, 2020. English. ⟨tel-02917021⟩

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