July 25, 2016
Journal Article

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

Xiu Yang
Luca Daniel
George Karniadakis
Ivan Oseledets
Zheng Zhang


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.

Revised: July 25, 2016 | Published: January 31, 2015


Zhang Z., X. Yang, I. Oseledets, G.E. Karniadakis, G.E. Karniadakis, and L. Daniel. 2015. "Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 34, no. 1:63-76. PNNL-SA-109438. doi:10.1109/TCAD.2014.2369505