Enabling HighDimensional Hierarchical Uncertainty Quantification by ANOVA and TensorTrain Decomposition
Abstract
Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some challenging stochastic circuits/systems that include highdimensional subsystems. Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the highlevel simulation. In this paper, we develop an efficient analysis of variancebased stochastic circuit/microelectromechanical systems simulator to efficiently extract the surrogate models at the low level. In order to avoid the curse of dimensionality, we employ tensortrain decomposition at the high level to construct the basis functions and Gauss quadrature points. As a demonstration, we verify our algorithm on a stochastic oscillator with four MEMS capacitors and 184 random parameters. This challenging example is efficiently simulated by our simulator at the cost of only 10min in MATLAB on a regular personal computer.
 Authors:
 Publication Date:
 Research Org.:
 Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1274892
 Report Number(s):
 PNNLSA109438
Journal ID: ISSN 02780070; KJ0401000
 DOE Contract Number:
 AC0576RL01830
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: IEEE Transations on ComputerAided Design of Integrated Circuits and Systems; Journal Volume: 34; Journal Issue: 1
 Country of Publication:
 United States
 Language:
 English
 Subject:
 ANOVA; gPC; UQ; MEMS; tensortrain
Citation Formats
Zhang, Zheng, Yang, Xiu, Oseledets, Ivan V., Karniadakis, George E., and Daniel, Luca. Enabling HighDimensional Hierarchical Uncertainty Quantification by ANOVA and TensorTrain Decomposition. United States: N. p., 2015.
Web. doi:10.1109/TCAD.2014.2369505.
Zhang, Zheng, Yang, Xiu, Oseledets, Ivan V., Karniadakis, George E., & Daniel, Luca. Enabling HighDimensional Hierarchical Uncertainty Quantification by ANOVA and TensorTrain Decomposition. United States. doi:10.1109/TCAD.2014.2369505.
Zhang, Zheng, Yang, Xiu, Oseledets, Ivan V., Karniadakis, George E., and Daniel, Luca. Thu .
"Enabling HighDimensional Hierarchical Uncertainty Quantification by ANOVA and TensorTrain Decomposition". United States.
doi:10.1109/TCAD.2014.2369505.
@article{osti_1274892,
title = {Enabling HighDimensional Hierarchical Uncertainty Quantification by ANOVA and TensorTrain Decomposition},
author = {Zhang, Zheng and Yang, Xiu and Oseledets, Ivan V. and Karniadakis, George E. and Daniel, Luca},
abstractNote = {Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some challenging stochastic circuits/systems that include highdimensional subsystems. Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the highlevel simulation. In this paper, we develop an efficient analysis of variancebased stochastic circuit/microelectromechanical systems simulator to efficiently extract the surrogate models at the low level. In order to avoid the curse of dimensionality, we employ tensortrain decomposition at the high level to construct the basis functions and Gauss quadrature points. As a demonstration, we verify our algorithm on a stochastic oscillator with four MEMS capacitors and 184 random parameters. This challenging example is efficiently simulated by our simulator at the cost of only 10min in MATLAB on a regular personal computer.},
doi = {10.1109/TCAD.2014.2369505},
journal = {IEEE Transations on ComputerAided Design of Integrated Circuits and Systems},
number = 1,
volume = 34,
place = {United States},
year = {Thu Jan 01 00:00:00 EST 2015},
month = {Thu Jan 01 00:00:00 EST 2015}
}

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