A computationally optimal randomized proper orthogonal decomposition technique
A computationally optimal randomized proper orthogonal decomposition technique
复制标题
计算最优随机适当正交分解技术
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
S. Chakravorty
中科院分区：
文献类型：
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作者：
Dan Yu;S. Chakravorty
本文研究了大系统的模型降阶问题，如通过偏微分方程离散化得到的系统。我们提出了一种计算上最优的随机本征正交分解（RPOD*）技术，通过使用高斯白色噪声扰动原始和伴随系统来获得降阶模型。我们表明，RPOD* 算法所需的计算量是数量级便宜的平衡适当的正交分解（BPOD）算法相比，而RPOD* 算法的性能优于BPOD。在需要最少数量的快照的意义上，它是最佳的。我们还将RPOD* 算法与随机投影算法联系起来。一个数值例子来说明的过程。
In this paper, we consider the model reduction problem of large-scale systems, such as systems obtained through the discretization of partial differential equations. We propose a computationally optimal randomized proper orthogonal decomposition (RPOD*) technique to obtain the reduced order model by perturbing the primal and adjoint system using Gaussian white noise. We show that the computations required by the RPOD* algorithm is orders of magnitude cheaper when compared to the balanced proper orthogonal decomposition (BPOD) algorithm while the performance of the RPOD* algorithm is better than BPOD. It is optimal in the sense that a minimal number of snapshots is needed. We also relate the RPOD* algorithm to random projection algorithms. One numerical example is given to illustrate the procedure.