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

Abstract

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.

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

References in corpus (4)

• Structured Sparse Principal Component Analysis
• Stochastic Testing Method for Transistor-Level Uncertainty Quantification Based on Generalized Polynomial Chaos
• Polynomial meta-models with canonical low-rank approximations: numerical insights and comparison to sparse polynomial chaos expansions
• Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition