EGU21-9566
https://doi.org/10.5194/egusphere-egu21-9566
EGU General Assembly 2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Machine learning based conditional mean filter: a non-linear extension of the ensemble Kalman filter 

Truong-Vinh Hoang, Sebastian Krumscheid, and Raul Tempone
Truong-Vinh Hoang et al.
  • RWTH-AAchen University, Chair of Mathematics for Uncertainty Quantification, Department of Mathematics, Germany (hoang@uq.rwth-aachen.de)

Filtering is an uncertainty quantification technique that refers to the inference of the states of dynamical systems from noisy observations. This work proposes a machine learning-based filtering method for tracking the high-dimensional non-Gaussian state-space models with non-linear dynamics and sparse observations. Our filter method is based on the conditional expectation mean filter and uses machine-learning techniques to approximate the conditional mean (CM). The contribution of this work is twofolds: (i) we demonstrate theoretically that the assimilated ensembles obtained using the ensemble conditional mean filter (EnCMF) provide a correct prediction of the posterior mean and have the optimal variance, and (ii) we implement the EnCMF using artificial neural networks, which has a significant advantage in representing non-linear functions that map between high-dimensionality domains, such as the CM. We implement the machine learning-based EnCMF for tracking the states of the Lorenz-63 and 96 systems under the chaotic regime. Numerical results show that the EnCMF outperforms the ensemble Kalman filter.

How to cite: Hoang, T.-V., Krumscheid, S., and Tempone, R.: Machine learning based conditional mean filter: a non-linear extension of the ensemble Kalman filter , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9566, https://doi.org/10.5194/egusphere-egu21-9566, 2021.

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