Repository: Freie Universit├Ąt Berlin, Math Department

Balanced data assimilation for highly-oscillatory mechanical systems

Reinhardt, M. and Hastermann, G. and Klein, R. and Reich, S. (2017) Balanced data assimilation for highly-oscillatory mechanical systems. Journal of Nonlinear Science . pp. 1-23. (Submitted)

[img]
Preview
PDF
861kB

Official URL: https://arxiv.org/abs/1708.03570

Abstract

Data assimilation algorithms are used to estimate the states of a dynamical system using partial and noisy observations. The ensemble Kalman filter has become a popular data assimilation scheme due to its simplicity and robustness for a wide range of application areas. Nevertheless, the ensemble Kalman filter also has limitations due to its inherent Gaussian and linearity assumptions. These limitations can manifest themselves in dynamically inconsistent state estimates. We investigate this issue in this paper for highly oscillatory Hamiltonian systems with a dynamical behavior which satisfies certain balance relations. We first demonstrate that the standard ensemble Kalman filter can lead to estimates which do not satisfy those balance relations, ultimately leading to filter divergence. We also propose two remedies for this phenomenon in terms of blended time-stepping schemes and ensemble-based penalty methods. The effect of these modifications to the standard ensemble Kalman filter are discussed and demonstrated numerically for two model scenarios. First, we consider balanced motion for highly oscillatory Hamiltonian systems and, second, we investigate thermally embedded highly oscillatory Hamiltonian systems. The first scenario is relevant for applications from meteorology while the second scenario is relevant for applications of data assimilation to molecular dynamics.

Item Type:Article
Additional Information:SFB 1114 Preprint 08/2017 in arXiv:1708.03570
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:2180
Deposited By: Silvia Hoemke
Deposited On:16 Jan 2018 13:47
Last Modified:16 Jan 2018 13:51

Repository Staff Only: item control page