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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/npg-2020-24
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-2020-24
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

  22 Jun 2020

22 Jun 2020

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This preprint is currently under review for the journal NPG.

Application of ensemble transform data assimilation methods for parameter estimation in nonlinear problems

Sangeetika Ruchi1, Svetlana Dubinkina1, and Jana de Wiljes2 Sangeetika Ruchi et al.
  • 1Centrum Wiskunde & Informatica, P.O. Box 94079, 1098 XG Amsterdam, the Netherlands
  • 2University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476, Potsdam, Germany

Abstract. Identification of unknown parameters on the basis of partial and noisy data is a challenging task in particular in high dimensional and nonlinear settings. Gaussian approximations to the problem, such as ensemble Kalman inversion, tend to be robust, computationally cheap and often produce astonishingly accurate estimations despite the inherently wrong underlying assumptions. Yet there is a lot of room for improvement specifically regarding the description of the associated statistics. The tempered ensemble transform particle filter is an adaptive sequential Monte Carlo method, where resampling is based on optimal transport mapping. Unlike ensemble Kalman inversion it does not require any assumptions regarding the posterior distribution and hence has shown to provide promising results for non-linear non-Gaussian inverse problems. However, the improved accuracy comes with the price of much higher computational complexity and the method is not as robust as the ensemble Kalman inversion in high dimensional problems. In this work, we add an entropy inspired regularisation factor to the underlying optimal transport problem that allows to considerably reduce the high computational cost via Sinkhorn iterations. Further, the robustness of the method is increased via an ensemble Kalman inversion proposal step before each update of the samples, which is also referred to as hybrid approach. The promising performance of the introduced method is numerically verified by testing it on a steady-state single-phase Darcy flow model with two different permeability configurations. The results are compared to the output of ensemble Kalman inversion, and Markov Chain Monte Carlo methods results are computed as a benchmark.

Sangeetika Ruchi et al.

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Sangeetika Ruchi et al.

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Latest update: 30 Sep 2020
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Short summary
To infer information of an unknown quantity that helps to understand an associated system better and to predict future outcomes, observations and a physical model that connects the data points to the unknown parameter are typically used as information sources. Yet this problem is often very challenging due to the fact that the unknown is generally high dimensional, the data is sparse and the model can be nonlinear. We propose a novel approach to address these challenges.
To infer information of an unknown quantity that helps to understand an associated system better...
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