4.7 Article

Sparsity-promoting elastic net method with rotations for high-dimensional nonlinear inverse problem

Journal

Publisher

ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2018.10.040

Keywords

Uncertainty quantification; Data assimilation; FISTA; Polynomial Chaos; Regularization; Ensemble Kalman filter

Funding

  1. National Natural Science Foundation of China [51728601, 41375115, 61572015]
  2. Open Research Project of the State Key Laboratory of Industrial Control Technology, Zhejiang University, China [ICT1600262]
  3. National Science Foundation [DMS-1555072, DMS-1736364, DMS-1821233]

Ask authors/readers for more resources

An elastic-net (EN) based polynomial chaos (PC) ensemble Kalman filter (PC-EnKF) with iterative PC-basis rotations is developed for high-dimensional nonlinear inverse modeling. To avoid the huge computational cost of estimating PC expansion coefficients and the Kalman gain matrix in PC-EnKF, this paper focuses mainly on solving the minimization problem of the elastic-net (EN) cost function with the fast iterative shrinkage-thresholding algorithm (FISTA). To further enhance the sparsity and accuracy, an iterative PC-basis rotation method is employed. When performing the rotation technique, two key issues need to be addressed to accommodate the computation of the inverse problem. One is the derivation of a new multi-dimensional random variable. This can be realized by exploring the construction of the gradient matrix used in a multi-parameter and vector-valued response model. The other issue is the selection of the number of iterative rotations during the process of each data assimilation, which can be addressed by resorting to a curve of sparsity versus the number of iterations. As for the regularization parameters, they can be tuned by calculating the information criteria (IC). Through the numerical examples, we demonstrate that EN-based PC-EnKF combined with the iterative PC-basis rotation method is well suited in the high-dimensional nonlinear inverse modeling, and has great potential in the high-dimensional nonlinear inverse modeling of real-world complex systems. (C) 2018 Elsevier B.V. All rights reserved.

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.7
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

No Data Available
No Data Available