Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Theory-Guided Autoencoders

被引:0
|
作者
Popov, Andrey A. [1 ]
Sandu, Adrian [1 ]
机构
[1] Computat Sci Lab, Dept Comp Sci, Blacksburg, VA 24060 USA
基金
美国国家科学基金会;
关键词
Bayesian inference; control variates; data assimilation; multifidelity ensemble Kalman filter; reduced order modeling; machine learning; surrogate models frontiers; CHEMICAL-DATA ASSIMILATION; PARAMETER-ESTIMATION; DECOMPOSITION; FORMULATION;
D O I
10.3389/fams.2022.904687
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities. This work extends the MFEnKF into to make use of a broader class of surrogate model such as those based on machine learning methods such as autoencoders non-linear couplings in between the model hierarchies. We identify the right-invertibility property for autoencoders as being a key predictor of success in the forecasting power of autoencoder-based reduced order models. We propose a methodology that allows us to construct reduced order surrogate models that are more accurate than the ones obtained via conventional linear methods. Numerical experiments with the canonical Lorenz'96 model illustrate that nonlinear surrogates perform better than linear projection-based ones in the context of multifidelity ensemble Kalman filtering. We additionality show a large-scale proof-of-concept result with the quasi-geostrophic equations, showing the competitiveness of the method with a traditional reduced order model-based MFEnKF.
引用
收藏
页数:18
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