论文标题
通过主动和秩适应性张量回归的高维不确定性定量
High-Dimensional Uncertainty Quantification via Active and Rank-Adaptive Tensor Regression
论文作者
论文摘要
基于随机光谱方法的不确定性定量遭受维数的诅咒。该问题最近通过低级张量方法来减轻。但是，在基于低量张量的不确定性量化中存在两个基本挑战：如何自动确定张量等级以及如何选择仿真样品。本文提出了一种新颖的张量回归方法来解决这两个挑战。我们的方法使用$ \ ell_ {q}/ \ ell_ {2} $ - 规范正规化来确定张量排名和估计的voronoi图来选择信息示例以进行仿真。提出的框架通过19 Dim Phonics带通滤波器和57 DIM CMOS环振荡器进行了验证，分别仅使用90和290个样品捕获高维不确定度。
Uncertainty quantification based on stochastic spectral methods suffers from the curse of dimensionality. This issue was mitigated recently by low-rank tensor methods. However, there exist two fundamental challenges in low-rank tensor-based uncertainty quantification: how to automatically determine the tensor rank and how to pick the simulation samples. This paper proposes a novel tensor regression method to address these two challenges. Our method uses an $\ell_{q}/ \ell_{2}$-norm regularization to determine the tensor rank and an estimated Voronoi diagram to pick informative samples for simulation. The proposed framework is verified by a 19-dim phonics bandpass filter and a 57-dim CMOS ring oscillator, capturing the high-dimensional uncertainty well with only 90 and 290 samples respectively.
