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arXiv 2009.019932020-09math.NAcs.NA

High-Dimensional Uncertainty Quantification via Active and Rank-Adaptive Tensor Regression

Zichang He, Zheng Zhang

备注：: Accepted by IEEE Electrical Performance of Electronic Packaging and Systems (EPEPS), 2020

英文摘要：

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.

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