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

TL;DR

This paper introduces a novel hierarchical uncertainty quantification framework combining ANOVA and tensor-train decomposition to efficiently simulate high-dimensional stochastic circuits, significantly reducing computational costs.

Contribution

It develops an efficient ANOVA-based surrogate modeling method at the low level and employs tensor-train decomposition at the high level to handle high-dimensional parameters.

Findings

Successfully simulated a stochastic oscillator with 184 parameters in 10 minutes.

Demonstrated efficiency and scalability of the proposed framework on complex MEMS circuits.

Reduced computational cost compared to traditional methods.

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 ANOVA-based stochastic circuit/MEMS simulator to extract efficiently 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 simulated efficiently by our simulator at the cost of only 10 minutes in MATLAB on a regular personal computer.