We present an Adaptive Parametrized-Background Data-Weak (APBDW) approach to the steady-state variational data assimilation (state estimation) problem for systems modeled by partial differential equations. The variational formulation is based on the Tikhonov regularization of the PBDW formulation [Y. Maday, A.T. Patera, J.D. Penn and M. Yano, Int. J. Numer. Meth. Eng. 102 (2015) 933–965] for pointwise noisy measurements. We propose an adaptive procedure based on a posteriori estimates of the state-estimation error to improve performance. We also present a priori estimates for the state-estimation error that motivate the approach and guide the adaptive procedure. We provide numerical experiments for a synthetic acoustic problem to illustrate the different elements of the methodology, and we consider an experimental thermal patch configuration to demonstrate the applicability of our approach to real physical systems.
Accepté le :
DOI : 10.1051/m2an/2017005
Mots clés : Variational data assimilation, parametrized partial differential equations, model order reduction, kernel methods
@article{M2AN_2017__51_5_1827_0, author = {Taddei, Tommaso}, title = {An {Adaptive} {Parametrized-Background} {Data-Weak} approach to variational data assimilation}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1827--1858}, publisher = {EDP-Sciences}, volume = {51}, number = {5}, year = {2017}, doi = {10.1051/m2an/2017005}, zbl = {1392.62125}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2017005/} }
TY - JOUR AU - Taddei, Tommaso TI - An Adaptive Parametrized-Background Data-Weak approach to variational data assimilation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 1827 EP - 1858 VL - 51 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2017005/ DO - 10.1051/m2an/2017005 LA - en ID - M2AN_2017__51_5_1827_0 ER -
%0 Journal Article %A Taddei, Tommaso %T An Adaptive Parametrized-Background Data-Weak approach to variational data assimilation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 1827-1858 %V 51 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2017005/ %R 10.1051/m2an/2017005 %G en %F M2AN_2017__51_5_1827_0
Taddei, Tommaso. An Adaptive Parametrized-Background Data-Weak approach to variational data assimilation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 5, pp. 1827-1858. doi : 10.1051/m2an/2017005. http://www.numdam.org/articles/10.1051/m2an/2017005/
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