An Adaptive Parametrized-Background Data-Weak approach to variational data assimilation

Taddei, Tommaso

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 5, pp. 1827-1858.

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 $L^2$ state-estimation error to improve performance. We also present a priori estimates for the $L^2$ 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.

Classification : 62-07, 93E24
Mots clés : Variational data assimilation, parametrized partial differential equations, model order reduction, kernel methods

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