Development of hp-inverse model by using generalized polynomial chaos
Development of hp-inverse model by using generalized polynomial chaos
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DOI：
10.1016/j.cma.2018.12.022
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发表时间：
2018-01
影响因子：
7.2
通讯作者：
K. Yeo;Y. Hwang;Xiao Liu;J. Kalagnanam
中科院分区：
文献类型：
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作者：
K. Yeo;Y. Hwang;Xiao Liu;J. Kalagnanam
我们提出了一个惠普逆模型估计一个光滑的，非负的源函数从有限数量的观察二维线性源反演问题。在具有均匀网格空间的矩形网格系统上，使用一组高斯径向基函数（GRBF），建立了标准的最小二乘逆模型。在这里，网格系统的选择被建模为一个随机变量和广义多项式混沌（gPC）的扩展被用来表示随机网格系统。它示出的卷积的gPC和GRBF提供了分层的基函数的线性源逆模型的HP-细化能力。我们提出了一个混合的l1和l2正则化，利用层次性质的基函数找到一个稀疏的解决方案。当数据数量有限时，Hp-逆模型比标准最小二乘逆模型具有优势。结果表明，即使当未知参数的个数（m）远大于数据个数（n）时，如mscinn> 40，hp-inverse模型仍能提供源函数的良好估计.
We present a h p-inverse model to estimate a smooth, non-negative source function from a limited number of observations for a two-dimensional linear source inversion problem. A standard least-square inverse model is formulated by using a set of Gaussian radial basis functions (GRBF) on a rectangular mesh system with a uniform grid space. Here, the choice of the mesh system is modeled as a random variable and the generalized polynomial chaos (gPC) expansion is used to represent the random mesh system. It is shown that the convolution of gPC and GRBF provides hierarchical basis functions for the linear source inverse model with the h p-refinement capability. We propose a mixed l 1 and l 2 regularization to exploit the hierarchical nature of the basis functions to find a sparse solution. The h p-inverse model has an advantage over the standard least-square inverse model when the number of data is limited. It is shown that the h p-inverse model provides a good estimate of the source function even when the number of unknown parameters (m) is much larger the number of data (n), eg, m∕ n> 40.