Articlegreen2019

High-Dimensional Uncertainty Quantification of Electronic and Photonic IC With Non-Gaussian Correlated Process Variations

31 citations0/0 files storedIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Probabilistic and Robust Engineering Design Low-power high-performance VLSI design Physical Unclonable Functions (PUFs) and Hardware Security

Abstract

Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters are mutually independent or Gaussian correlated, which is rarely true in real applications. For instance, in chip manufacturing, many process variations are actually correlated. Recently, some techniques have been developed to handle non-Gaussian correlated random parameters, but they are time-consuming for high-dimensional problems. We present a new framework to solve uncertainty quantification problems with many non-Gaussian correlated uncertainties. First, we propose a set of smooth basis functions to well capture the impact of non-Gaussian correlated process variations. We develop a tensor approach to compute these basis functions in a high-dimension setting. Second, we investigate the theoretical aspect and practical implementation of a sparse solver to compute the coefficients of all basis functions. We provide some theoretical analysis for the exact recovery condition and error bound of this sparse solver in the context of uncertainty quantification. We present three adaptive sampling approaches to improve the performance of the sparse solver. Finally, we validate our methods by synthetic and practical electronic/photonic ICs with 19 to 57 non-Gaussian correlated variation parameters. Our approach outperforms Monte Carlo by thousands of times in terms of efficiency. It can also accurately predict the output density functions with multiple peaks caused by non-Gaussian correlations, which are hard to capture by existing methods.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 31 citations exist upstream.

References

2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2005High-Order Collocation Methods for Differential Equations with Random Inputs 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure 2014Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies 2010An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations 2013Stochastic Testing Method for Transistor-Level Uncertainty Quantification Based on Generalized Polynomial Chaos 1991Stochastic Finite Element Method: Response Statistics 2018Sparse polynomial chaos expansions via compressed sensing and D-optimal design

Cited by

2020A Perturbative Stochastic Galerkin Method for the Uncertainty Quantification of Linear Circuits 2021Fast Stochastic Surrogate Modeling via Rational Polynomial Chaos Expansions and Principal Component Analysis

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.