Geodesic
Statistical inference for partial differential equations
Emmanuel Grenier1 ; Marc Hoffmann2 ; Tony Lelièvre3 ; Violaine Louvet4 ; Clémentine Prieur5 ; Nabil Rachdi6 ; Paul Vigneaux1
1 ENS Lyon, UPMA; INRIA, Project-team NUMED
2 Paris Dauphine, CEREMADE
3 Université Paris-Est, ENPC, CERMICS; INRIA, Project-team MICMAC
4 Université de Lyon, ICJ; INRIA, Project-team NUMED
5 Université Grenoble Alpes, LJK; INRIA, Project-team MOISE
6 EADS Innovation Works
ESAIM. Proceedings, Tome 45 (2014), pp. 178-188.

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Many physical phenomena are modeled by parametrized PDEs. The poor knowledge on the involved parameters is often one of the numerous sources of uncertainties on these models. Some of these parameters can be estimated, with the use of real world data. The aim of this mini-symposium is to introduce some of the various tools from both statistical and numerical communities to deal with this issue. Parametric and non-parametric approaches are developed in this paper. Some of the estimation procedures require many evaluations of the initial model. Some interpolation tools and some greedy algorithms for model reduction are therefore also presented, in order to reduce time needed for running the model.
DOI : 10.1051/proc/201445018

Emmanuel Grenier 1 ; Marc Hoffmann 2 ; Tony Lelièvre 3 ; Violaine Louvet 4 ; Clémentine Prieur 5 ; Nabil Rachdi 6 ; Paul Vigneaux 1

1 ENS Lyon, UPMA; INRIA, Project-team NUMED
2 Paris Dauphine, CEREMADE
3 Université Paris-Est, ENPC, CERMICS; INRIA, Project-team MICMAC
4 Université de Lyon, ICJ; INRIA, Project-team NUMED
5 Université Grenoble Alpes, LJK; INRIA, Project-team MOISE
6 EADS Innovation Works 
@article{EP_2014_45_a18,
     author = {Emmanuel Grenier and Marc Hoffmann and Tony Leli\`evre and Violaine Louvet and Cl\'ementine Prieur and Nabil Rachdi and Paul Vigneaux},
     title = {Statistical inference for partial differential equations},
     journal = {ESAIM. Proceedings},
     pages = {178--188},
     publisher = {mathdoc},
     volume = {45},
     year = {2014},
     doi = {10.1051/proc/201445018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201445018/}
}
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AU  - Violaine Louvet
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%T Statistical inference for partial differential equations
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Emmanuel Grenier; Marc Hoffmann; Tony Lelièvre; Violaine Louvet; Clémentine Prieur; Nabil Rachdi; Paul Vigneaux. Statistical inference for partial differential equations. ESAIM. Proceedings, Tome 45 (2014), pp. 178-188. doi : 10.1051/proc/201445018. http://geodesic.mathdoc.fr/articles/10.1051/proc/201445018/

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