Combined state and parameter estimation in level-set methods

JOURNAL OF COMPUTATIONAL PHYSICS

卷:399

Article

Yu, Hans¹  Juniper, Matthew R.¹  Magri, Luca^1,2 

[1] Univ Cambridge, Dept Engn, Trumpington St, Cambridge CB2 1PZ, England

[2] Tech Univ Munich, Inst Adv Study, Lichtenbergstr 2a, D-85748 Garching, Germany

关键词: Data assimilation;    Ensemble Kalman filter;    Level-set method;    Parameter estimation;    Uncertainty quantification;   

DOI  :  10.1016/j.jcp.2019.108950

来源: Elsevier

【 摘 要 】

Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous learning algorithm for state and parameter estimation with level-set methods. A Bayesian approach based on data assimilation is introduced. Data assimilation is enabled by the ensemble Kalman filter and smoother, which are used in their probabilistic formulations. The level-set data assimilation framework is verified in one-dimensional and two-dimensional test cases, where state estimation, parameter estimation and uncertainty quantification are performed. The statistical performance of the proposed ensemble Kalman filter and smoother is quantified by twin experiments. In the twin experiments, the combined state and parameter estimation fully recovers the reference solution, which validates the proposed algorithm. The level-set data assimilation framework is then applied to the prediction of the nonlinear dynamics of a forced premixed flame, which exhibits the formation of sharp cusps and intricate topological changes, such as pinch-off events. The proposed physics-informed statistical learning algorithm opens up new possibilities for making reduced-order models of interfaces quantitatively predictive, any time that reference data is available. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free