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Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition

Author(s)
Oseledets, Ivan V.; Karniadakis, George E.; Daniel, Luca; Zhang, Zheng; Yang, Xiu
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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 high-dimensional 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 high-level simulation. In this paper, we develop an efficient analysis of variance-based 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 tensor-train 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.
Date issued
2014-11
URI
http://hdl.handle.net/1721.1/99952
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Research Laboratory of Electronics
Journal
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Zheng Zhang, Xiu Yang, Ivan V. Oseledets, George E. Karniadakis, and Luca Daniel. “Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition.” IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 34, no. 1 (January 2015): 63–76.
Version: Author's final manuscript
ISSN
0278-0070
1937-4151

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