Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition
Name
Daniel_Enabling high.pdf
Size
1.37 MB
Format
Adobe PDF
Checksum (MD5)
cc3ddbd91fb5cb7f7b74a2fe7bc5362a
Author(s)
Oseledets, Ivan V.
Karniadakis, George E.
Daniel, Luca
Zhang, Zheng
Yang, Xiu
Date Issued
November 2014
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Research Laboratory of Electronics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/TCAD.2014.2369505
