A Big-Data Approach to Handle Process Variations: Uncertainty Quantification by Tensor Recovery

TL;DR

This paper introduces a big-data tensor recovery method for high-dimensional uncertainty quantification in nano-scale device simulations, significantly reducing computational costs compared to traditional stochastic methods.

Contribution

It proposes a novel tensor recovery approach that enables efficient uncertainty quantification with thousands of random parameters using limited simulation samples.

Findings

Successfully extended tensor-product stochastic collocation to over 50 random parameters

Achieved accurate uncertainty quantification with only hundreds of samples

Demonstrated significant computational savings over traditional methods

Abstract

Stochastic spectral methods have become a popular technique to quantify the uncertainties of nano-scale devices and circuits. They are much more efficient than Monte Carlo for certain design cases with a small number of random parameters. However, their computational cost significantly increases as the number of random parameters increases. This paper presents a big-data approach to solve high-dimensional uncertainty quantification problems. Specifically, we simulate integrated circuits and MEMS at only a small number of quadrature samples, then, a huge number of (e.g., $1.5 \times 10^{27}$) solution samples are estimated from the available small-size (e.g., $500$) solution samples via a low-rank and tensor-recovery method. Numerical results show that our algorithm can easily extend the applicability of tensor-product stochastic collocation to IC and MEMS problems with over 50 random parameters, whereas the traditional algorithm can only handle several random parameters.