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arXiv · 2212.07719

Time-limited Balanced Truncation for Data Assimilation Problems

Josie König·Melina A. Freitag
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Abstract

Balanced truncation is a well-established model order reduction method which has been applied to a variety of problems. Recently, a connection between linear Gaussian Bayesian inference problems and the system-theoretic concept of balanced truncation has been drawn. Although this connection is new, the application of balanced truncation to data assimilation is not a novel idea: it has already been used in four-dimensional variational data assimilation (4D-Var). This paper discusses the application of balanced truncation to linear Gaussian Bayesian inference, and, in particular, the 4D-Var method, thereby strengthening the link between systems theory and data assimilation further. Similarities between both types of data assimilation problems enable a generalisation of the state-of-the-art approach to the use of arbitrary prior covariances as reachability Gramians. Furthermore, we propose an enhanced approach using time-limited balanced truncation that allows to balance Bayesian inference for unstable systems and in addition improves the numerical results for short observation periods.

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Josie König, Melina A. Freitag. 2022-12-15. Time-limited Balanced Truncation for Data Assimilation Problems. https://doi.org/10.1007/s10915-023-02358-4

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