Sparsity-promoting elastic net method with rotations for high-dimensional nonlinear inverse problem
Sparsity-promoting elastic net method with rotations for high-dimensional nonlinear inverse problem
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高维非线性反问题的稀疏促进旋转弹性网法
DOI：
10.1016/j.cma.2018.10.040
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发表时间：
2019-03
期刊：
影响因子：
--
通讯作者：
Chao Xu
中科院分区：
文献类型：
--
作者：
王曰朋;Lanlan Rena;Zongyuan Zhang;Guang Lin;Chao Xu
提出了一种基于弹性网络（EN）的迭代多项式混沌（PC）系综卡尔曼滤波器（PC-EnKF）。为了避免PC-EnKF中估计PC展开系数和卡尔曼增益矩阵的巨大计算开销，本文主要研究了用快速迭代收缩阈值算法（FISTA）求解弹性网络（EN）代价函数的最小化问题。为了进一步提高稀疏性和精度，采用迭代PC基旋转方法。当执行旋转技术时，需要解决两个关键问题以适应逆问题的计算。一个是一个新的多维随机变量的推导。这可以通过探索在多参数和向量值响应模型中使用的梯度矩阵的构造来实现。另一个问题是在每次数据同化过程中迭代旋转次数的选择，这可以通过采用稀疏度与迭代次数的曲线来解决。对于正则化参数，可以通过计算信息准则（IC）来调整。通过数值算例，证明了基于EN的PC-EnKF结合迭代PC基旋转方法非常适合于高维非线性逆建模，在实际复杂系统的高维非线性逆建模中具有很大的潜力。
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.
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DOI：
10.1016/j.jcp.2014.02.024
发表时间：
2013-08
期刊：
J. Comput. Phys.
影响因子：
--
作者：
Jigen Peng;Jerrad Hampton;A. Doostan
通讯作者：
Jigen Peng;Jerrad Hampton;A. Doostan
DOI：
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期刊：
Comput. Electron. Agric.
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2014-02
期刊：
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影响因子：
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作者：
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DOI：
10.1109/icip.2005.1530172
发表时间：
2005-11
期刊：
IEEE International Conference on Image Processing 2005
影响因子：
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作者：
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通讯作者：
Mário A. T. Figueiredo;Robert D. Nowak
影响因子：
3.2
作者：
J. Srinivasan;G. Smith
通讯作者：
J. Srinivasan;G. Smith