# Population parametrization of costly black box models using iterations between SAEM algorithm and kriging

## Abstract

In this article we focus on parametrization of black box models from repeated measurements among several individuals (population parametrization). We introduce a variant of the SAEM algorithm, called KSAEM algorithm, which couples the standard SAEM algorithm with the dynamic construction of an approximate metamodel. The costly evaluation of the genuine black box is replaced by a kriging step, using a basis of precomputed values, basis which is enlarged during SAEM algorithm to improve the accuracy of the metamodel in regions of interest.

- Authors:

- Univ Lyon, ENS de Lyon, CNRS UMR 5669, UMPA (France)
- Univ Lyon, CNRS UMR 5208, Ecole Centrale de Lyon, ICJ (France)
- GRICAD, Universite Grenoble Alpes (France)
- Universite Grenoble Alpes, LJK (France)

- Publication Date:

- OSTI Identifier:
- 22769391

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; BOX MODELS; KRIGING; NONLINEAR PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS

### Citation Formats

```
Grenier, Emmanuel, Helbert, Celine, Louvet, Violaine, Samson, Adeline, and Vigneaux, Paul.
```*Population parametrization of costly black box models using iterations between SAEM algorithm and kriging*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0337-5.

```
Grenier, Emmanuel, Helbert, Celine, Louvet, Violaine, Samson, Adeline, & Vigneaux, Paul.
```*Population parametrization of costly black box models using iterations between SAEM algorithm and kriging*. United States. doi:10.1007/S40314-016-0337-5.

```
Grenier, Emmanuel, Helbert, Celine, Louvet, Violaine, Samson, Adeline, and Vigneaux, Paul. Thu .
"Population parametrization of costly black box models using iterations between SAEM algorithm and kriging". United States. doi:10.1007/S40314-016-0337-5.
```

```
@article{osti_22769391,
```

title = {Population parametrization of costly black box models using iterations between SAEM algorithm and kriging},

author = {Grenier, Emmanuel and Helbert, Celine and Louvet, Violaine and Samson, Adeline and Vigneaux, Paul},

abstractNote = {In this article we focus on parametrization of black box models from repeated measurements among several individuals (population parametrization). We introduce a variant of the SAEM algorithm, called KSAEM algorithm, which couples the standard SAEM algorithm with the dynamic construction of an approximate metamodel. The costly evaluation of the genuine black box is replaced by a kriging step, using a basis of precomputed values, basis which is enlarged during SAEM algorithm to improve the accuracy of the metamodel in regions of interest.},

doi = {10.1007/S40314-016-0337-5},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 1,

volume = 37,

place = {United States},

year = {2018},

month = {3}

}

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