Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Zhang, Zheng; Batselier, Kim; Liu, Haotian; Daniel, Luca; Wong, Ngai

doi:10.1109/tcad.2016.2618879

Cited by 41 publications

(26 citation statements)

References 123 publications

(155 reference statements)

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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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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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“…However, specific limitations and challenges arise in the application of the PC expansion when a high number of random variables is considered [93]. Note that the number of terms M + 1 in a PC model increases rapidly with respect to the maximum degree of the polynomial basis functions P (also called order of the expansion) and the number of random parameter N, as shown in Equation (15).…”

Section: High-dimensional Problemsmentioning

confidence: 99%

“…Indeed, the application of such techniques has grown rapidly: micromagnetics [96][97][98], model order reduction [99,100], big data [101][102][103], signal processing [104][105][106][107], control design [108,109], and electronic design automation [93].…”

Section: Efficient Sampling Strategies For High-dimensional Problemsmentioning

confidence: 99%

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Review of Polynomial Chaos-Based Methods for Uncertainty Quantification in Modern Integrated Circuits

2018

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Advances in manufacturing process technology are key ensembles for the production of integrated circuits in the sub-micrometer region. It is of paramount importance to assess the effects of tolerances in the manufacturing process on the performance of modern integrated circuits. The polynomial chaos expansion has emerged as a suitable alternative to standard Monte Carlo-based methods that are accurate, but computationally cumbersome. This paper provides an overview of the most recent developments and challenges in the application of polynomial chaos-based techniques for uncertainty quantification in integrated circuits, with particular focus on high-dimensional problems.

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“…In recent years, there has been significant improvement to address this challenge. Representative techniques include (but are not limited to) compressive sensing [17,18], analysis of variance [15,19], stochastic model order reduction [20], hierarchical methods [15,21,22] and tensor computation [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Uncertainty quantification of electronic and photonic ICs with non-Gaussian correlated process variations

Cui

Zhang

2018

Proceedings of the International Conference on Computer-Aided Design

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Since the invention of generalized polynomial chaos in 2002, uncertainty quantification has impacted many engineering fields, including variation-aware design automation of integrated circuits and integrated photonics. Due to the fast convergence rate, the generalized polynomial chaos expansion has achieved orders-of-magnitude speedup than Monte Carlo in many applications. However, almost all existing generalized polynomial chaos methods have a strong assumption: the uncertain parameters are mutually independent or Gaussian correlated. This assumption rarely holds in many realistic applications, and it has been a long-standing challenge for both theorists and practitioners.This paper propose a rigorous and efficient solution to address the challenge of non-Gaussian correlation. We first extend generalized polynomial chaos, and propose a class of smooth basis functions to efficiently handle non-Gaussian correlations. Then, we consider high-dimensional parameters, and develop a scalable tensor method to compute the proposed basis functions. Finally, we develop a sparse solver with adaptive sample selections to solve high-dimensional uncertainty quantification problems. We validate our theory and algorithm by electronic and photonic ICs with 19 to 57 non-Gaussian correlated variation parameters. The results show that our approach outperforms Monte Carlo by 2500× to 3000× in terms of efficiency. Moreover, our method can accurately predict the output density functions with multiple peaks caused by non-Gaussian correlations, which is hard to handle by existing methods.Based on the results in this paper, many novel uncertainty quantification algorithms can be developed and can be further applied to a broad range of engineering domains.

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Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Cited by 41 publications

References 123 publications

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

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

Review of Polynomial Chaos-Based Methods for Uncertainty Quantification in Modern Integrated Circuits

Uncertainty quantification of electronic and photonic ICs with non-Gaussian correlated process variations

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