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

arXiv: https://arxiv.org/abs/1603.06119 · HTML: https://mlsanity.com/paper/1603.06119/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2016.

## Built on by (most cited first, 1 of 1)

- [High-Dimensional Uncertainty Quantification via Tensor Regression with Rank Determination and Adaptive Sampling](https://mlsanity.com/paper/2103.17236/) (2021)

## Abstract (arXiv)

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 × 1027) 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.