Feasibility of DEIM for retrieving the initial field via dimensionality reduction

JOURNAL OF COMPUTATIONAL PHYSICS

卷:429

Article

Wang, Yuepeng¹  Ding, Xuemei¹  Hu, Kun¹  Fang, Fangxin²  Navon, I. M.³  Lin, Guang^4,5 

[1] Nanjing Univ Informat Sci & Technol NUIST, Sch Math & Stat, Nanjing 210044, Peoples R China

[2] Imperial Coll London, Dept Earth Sci & Engn, Prince Consort Rd, London SW7 2AZ, England

[3] Florida State Univ, Dept Sci Comp, Tallahassee, FL 32306 USA

[4] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[5] Purdue Univ, Sch Mech Engn, W Lafayette, IN 47907 USA

关键词: Data assimilation;    Discrete empirical interpolation method (DEIM);    Uncertainty quantification;    Polynomial chaos;    Ensemble Kalman filter;   

DOI  :  10.1016/j.jcp.2020.110005

来源: Elsevier

【 摘 要 】

When parameter estimation is solved in a high-dimensional space, the dimensionality reduction strategy becomes the primary consideration for alleviating the tremendous computational cost. In the present study, the discrete empirical interpolation method (DEIM) is explored to retrieve the initial condition (IC) by combining the polynomial chaos (PC) based ensemble Kalman filter (i.e. PC-EnKF), where a non-intrusive PC expansion is considered as a surrogate model in place of the forward model in the prediction step of the ensemble Kalman filter, resulting in fewer forward model integrations but with a comparable accuracy as Monte Carlo-based approaches. The DEIM acts as a hyper-reduction tool to provide the low-dimensional input for the high-dimensional initial field, which can be reconstructed using the information on the sparse interpolation grid points that is adaptively obtained through PC-EnKF data assimilation method. Thus an innovative framework to reconstruct the IC is developed. The detailed procedure at each assimilation iteration includes: the determination of the spatial interpolation points, the estimation of the initial values on the interpolation locations using the optimal observations, and the reconstruction of IC in the full space. The current study uses the reconstruction field of initial conditions of the Navier-Stokes equations as an example to illustrate the efficacy of our method. The experimental results demonstrate the proposed algorithm achieves a satisfactory reconstruction for the initial field. The proposed method helps to extend the applicable area of DEIM in solving inverse problems. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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