ENSEMBLE KALMAN FILTER FOR MULTISCALE INVERSE PROBLEMS
ENSEMBLE KALMAN FILTER FOR MULTISCALE INVERSE PROBLEMS
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DOI：
10.1137/20m1348431
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发表时间：
2020-01-01
影响因子：
1.6
通讯作者：
Zanoni, Andrea
中科院分区：
文献类型：
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作者：
Abdulle, Assyr;Garegnani, Giacomo;Zanoni, Andrea
提出了一种基于集合卡尔曼滤波的多尺度椭圆型偏微分方程反问题的新算法。我们的方法是基于数值均匀化和有限元离散化，并允许我们恢复一个高度振荡张量从测量的多尺度解决方案在计算上便宜的方式。近似解的性质进行了分析，相对于多尺度和离散化参数，收敛结果被证明是成立的。从贝叶斯的角度重新解释的解决方案，并证明了收敛的近似条件后验分布相对于Wasserstein距离。数值实验验证了我们的方法，特别强调建模误差和计算成本。
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and allows us to recover a highly oscillatory tensor from measurements of the multiscale solution in a computationally inexpensive manner. The properties of the approximate solution are analyzed with respect to the multiscale and discretization parameters, and a convergence result is shown to hold. A reinterpretation of the solution from a Bayesian perspective is provided, and convergence of the approximate conditional posterior distribution is proved with respect to the Wasserstein distance. A numerical experiment validates our methodology, with a particular emphasis on modeling error and computational cost.