Stochastic testing simulator for integrated circuits and MEMS: Hierarchical and sparse techniques

Zhang, Zheng; Yang, Xiu; Marucci, Giovanni; Maffezzoni, P.; Ibrahim, Rania A.; Elfadel, Ibrahim Abe M.; Karniadakis, George Em; Daniel, Luca

doi:10.1109/cicc.2014.6946009

Cited by 35 publications

(38 citation statements)

References 45 publications

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“…All parameters are assumed Gaussian with their standard deviations being 25% of the norminal values. In this example, the ANOVA-based stochastic testing solver [17] is combined with the deterministic MRI solver [15] to obtain a sparse generalized polynomial-chaos expansion for the loop antenna impedance, and the tensor-train-based three-term recurrence relation is employed to construct some orthonormal polynomials [21]. The numerical results are plotted in Fig.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Finally, the generalized polynomialchaos expansion (1) is obtained by interpolation [7]. For high-dimensional problems, we use the sparse stochastic testing simulator [17] to generate a representation for y. This simulator uses analysis of variance (ANOVA) to decompose y into some low-dimensional functions of the uncertainties x, then the importance of each random parameter and the couplings among them are estimated on-the-fly, giving a sparse generalized polynomial-chaos expansion for y.…”

Section: A Stochastic Electromagnetic Field Solver For Mri Problemsmentioning

confidence: 99%

See 1 more Smart Citation

Maximum-Entropy Density Estimation for MRI Stochastic Surrogate Models

Zhang

Farnoosh

Klemas

et al. 2014

Antennas Wirel. Propag. Lett.

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Abstract-Stochastic spectral methods can generate accurate compact stochastic models for electromagnetic problems with material and geometric uncertainties. This letter presents an improved implementation of the maximum-entropy algorithm to compute the density function of an obtained generalized polynomial chaos expansion in Magnetic Resonance Imaging (MRI) applications. Instead of using statistical moments, we show that the expectations of some orthonormal polynomials can be better constraints for the optimization flow. The proposed algorithm is coupled with a finite element-boundary element method (FEM-BEM) domain decomposition field solver to obtain a robust computational prototyping for MRI problems with low and high dimensional uncertainties.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: A Stochastic Electromagnetic Field Solver For Mri Problemsmentioning

confidence: 99%

Maximum-Entropy Density Estimation for MRI Stochastic Surrogate Models

Zhang

Farnoosh

Klemas

et al. 2014

Antennas Wirel. Propag. Lett.

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“…After constructing the basis functions {Ψ α (ξ)} p |α|=0 , we need to compute the weights (or coefficients) {c α }. For the independent case, many high-dimensional solvers have been developed, such as compressed sensing [33], [34], analysis of variance [21], [35], model order reduction [36], hierarchical methods [21], [37], [38], and tensor computation [38]- [40]. For the non-Gaussian correlated case discussed in this paper, we employ a sparse solver to obtain the coefficients.…”

Section: A Sparse Solver: Why and How Does It Work?mentioning

confidence: 99%

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

Cui

Zhang

2020

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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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 timeconsuming for high-dimensional problems. We present a new framework to solve uncertainty quantification problems with many non-Gaussian correlated uncertainties. Firstly, 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 highdimension setting. Secondly, 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.Index Terms-High dimensionality, uncertainty quantification, electronic and photonic IC, non-Gaussian correlation, process variations, tensor, sparse solver, adaptive sampling.

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“…Then it uses a model selection algorithm to build a suitable regression model for all the responses. More Recently, several statistical circuit simulator based on uncertainty quantification have been successfully applied to avoid the huge number of repeated simulations in conventional Monte Carlo flows [5]- [9].…”

Section: Introductionmentioning

confidence: 99%

Statistical Library Characterization using Belief Propagation across Multiple Technology Nodes

Liu

Saxena

Hess

et al. 2015

Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE), 2015

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Abstract-In this paper, we propose a novel flow to enable computationally efficient statistical characterization of delay and slew in standard cell libraries. The distinguishing feature of the proposed method is the usage of a limited combination of output capacitance, input slew rate and supply voltage for the extraction of statistical timing metrics of an individual logic gate. The efficiency of the proposed flow stems from the introduction of a novel, ultra-compact, nonlinear, analytical timing model, having only four universal regression parameters. This novel model facilitates the use of maximum-a-posteriori belief propagation to learn the prior parameter distribution for the parameters of the target technology from past characterizations of library cells belonging to various other technologies, including older ones. The framework then utilises Bayesian inference to extract the new timing model parameters using an ultra-small set of additional timing measurements from the target technology. The proposed method is validated and benchmarked on several production-level cell libraries including a state-of-the-art 14-nm technology node and a variation-aware, compact transistor model. For the same accuracy as the conventional lookup-table approach, this new method achieves at least 15x reduction in simulation runs.

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Stochastic testing simulator for integrated circuits and MEMS: Hierarchical and sparse techniques

Cited by 35 publications

References 45 publications

Maximum-Entropy Density Estimation for MRI Stochastic Surrogate Models

Maximum-Entropy Density Estimation for MRI Stochastic Surrogate Models

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

Statistical Library Characterization using Belief Propagation across Multiple Technology Nodes

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