Combining ensemble Kalman filter and multiresolution analysis for efficient assimilation into adaptive mesh models

Abstract

A new approach is developed for efficient data assimilation into adaptive mesh simulations with the ensemble Kalman filter (EnKF). The EnKF is combined with a wavelet-based multi-resolution analysis (MRA) scheme, namely to enable robust and efficient assimilation in the context of reducedcomplexity, adaptive spatial discretization. The wavelet representation of the solution enables us to use a different meshes that are individually adapted to the corresponding member of the EnKF ensemble. The analysis step of the EnKF is then performed by involving coarsening, refinement, and projection operations on the members. Depending on the choice of these operations, five variants of the MRA-EnKF are introduced, and tested on the one dimensional Burgers equation with periodic boundary condition. The numerical results suggest that, given an appropriate tolerance value for the coarsening operation, four out of the five proposed schemes significantly reduce the computational complexity of the data assimilation, with marginal accuracy loss with respect to the reference EnKF solution. Overall, the proposed framework offers the possibility of capitalizing on the advantages adaptive mesh techniques, and the flexibility of choosing suitable context-oriented criteria for efficient data assimilation.

Optimized parametric inference for the inner loop of the Multigrid Ensemble Kalman Filter

“…2. This method is reminiscent of multilevel [20,21,37,22] and multifidelity [38,23] ensemble techniques for data assimilation. Our approach differs by the use of surrogate observations issued from the fine grid resolution to infer the correction parameters of the numerical integration scheme.…”

“…Applications for scale resolving unstationary flows such as direct numerical simulation (DNS) and large eddy simulation (LES) are much more rare in the literature, because of the computational resources required [10,19] to generate an acceptably large database to perform a converged parametric inference. Alternative strategies recently explored to reduce the computational costs deal with multilevel [20,21,22] / multifidelity [23] ensemble applications.…”

A multigrid/ensemble Kalman Filter strategy for assimilation of unsteady flows

“…-The observations are sampled each 30 time steps of the reference simulation on the space domain [0, 1] (80 sensors) and on the time window [10,29]. The observations are sampled as soon as the flow is fully developed.…”

“…The EnKF error covariance matrix reconstruction is performed using information from a number of ensemble members which are generated over a coarse level mesh of a multigrid approach. This procedure is reminiscent of reduced order / multilevel applications of EnKF strategy reported in the literature [28,29,30,31]. However, the state estimation obtained at the coarse level is used to obtain a single solution calculated on a high resolution mesh grid, similarly to the work by Debreu et al [32] for variational DA.…”

A non‐Gaussian Bayesian filter for sequential data assimilation with non‐intrusive polynomial chaos expansion

“…Nevertheless, the intrusive DO scheme makes widespread adoption time consuming. While there have been several papers on Bayesian inference of parameters from PCE models, [22][23][24][25][26] the advantages posed by PCE in quantifying uncertainty and the availability of non-intrusive numerical schemes and packages 18,27 have only been rarely utilized in sequential non-Gaussian data assimilation. 28 The present article aims to fill this gap.…”