High-Dimensional Uncertainty Quantification via Active and Rank-Adaptive Tensor Regression
| Autor: | Zheng Zhang, Zichang He |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Rank (linear algebra)
Computer science 010103 numerical & computational mathematics 02 engineering and technology Numerical Analysis (math.NA) 01 natural sciences Regularization (mathematics) Regression 020202 computer hardware & architecture Tensor (intrinsic definition) 0202 electrical engineering electronic engineering information engineering FOS: Mathematics Mathematics - Numerical Analysis 0101 mathematics Uncertainty quantification Spectral method Voronoi diagram Algorithm Curse of dimensionality |
| DOI: | 10.48550/arxiv.2009.01993 |
| Popis: | 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. Comment: Accepted by IEEE Electrical Performance of Electronic Packaging and Systems (EPEPS), 2020 |
| Databáze: | OpenAIRE |
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