1. Gaussian process metamodeling of functional-input code for coastal flood hazard assessment
- Author
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Jeremy Rohmer, José Betancourt, Thierry Klein, Déborah Idier, Rodrigo Pedreros, François Bachoc, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Ecole Nationale de l'Aviation Civile (ENAC), Bureau de Recherches Géologiques et Minières (BRGM) (BRGM), Agence Nationale de la Recherche, ANR-16-CE04-0011,RISCOPE,Système d'alerte de submersion côtière centré sur le risque(2016), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-PRES Université de Toulouse-Université Toulouse III - Paul Sabatier (UPS), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UPS), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-PRES Université de Toulouse-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Mathematical optimization ,Computer science ,Gaussian ,Computer experiments ,0211 other engineering and technologies ,Gaussian processes ,[SDU.STU]Sciences of the Universe [physics]/Earth Sciences ,02 engineering and technology ,Metamodeling ,Industrial and Manufacturing Engineering ,symbols.namesake ,[STAT.ML]Statistics [stat]/Machine Learning [stat.ML] ,[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] ,Robustness (computer science) ,Gaussian process ,Safety, Risk, Reliability and Quality ,Projection (set theory) ,021110 strategic, defence & security studies ,021103 operations research ,[SDE.IE]Environmental Sciences/Environmental Engineering ,Dimensionality reduction ,Model selection ,Computer experiment ,Functional inputs ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,[SDE]Environmental Sciences ,symbols ,Computer code experiments - Abstract
International audience; This paper investigates the construction of a metamodel for coastal flooding early warning at the peninsula of Gâvres, France. The code under study is an hydrodynamic model which receives time-varying maritime conditions as inputs. We concentrate on Gaussian pocess metamodels to emulate the behavior of the code. To model the inputs we make a projection of them onto a space of lower dimension. This setting gives rise to a model selection methodology which we use to calibrate four characteristics of our functional-input metamodel: (i) the family of basis functions to project the inputs; (ii) the projection dimension; (iii) the distance to measure similarity between functional input points; and (iv) the set of functional predictors to keep active. The proposed methodology seeks to optimize these parameters for metamodel predictability, at an affordable computational cost. A comparison to a dimensionality reduction approach based on the projection error of the input functions only showed that the latter may lead to unnecessarily large projection dimensions. We also assessed the adaptability of our methodology to changes in the number of training and validation points. The methodology proved its robustness by finding the optimal solution for most of the instances, while being computationally efficient.
- Published
- 2020
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