Efficient State/Parameter Estimation in Nonlinear Unsteady PDEs by a Reduced Basis Ensemble Kalman Filter

Abstract

The ensemble Kalman filter is a computationally efficient technique for solving state and/or parameter estimation problems in the framework of statistical inversion when relying on a Bayesian paradigm. Unfortunately, its cost may become moderately large for systems described by nonlinear time-dependent PDEs, because of the cost entailed by each PDE query. In this paper we propose a reduced basis ensemble Kalman filter technique to address the above problems. The reduction stage yields intrinsic approximation errors, whose propagation through the filtering process might affect the accuracy of state/parameter estimates. For an efficient evaluation of these errors, we equip our reduced basis ensemble Kalman filter with a reduction error model (or error surrogate). The latter is based on ordinary kriging for functional-valued data, to gauge the effect of state reduction on the whole filtering process. The accuracy and efficiency of the resulting method is then verified on the estimation of uncertain parameter...