Sparse Linear Regression (SPLINER) Approach for Efficient Multidimensional Uncertainty Quantification of High-Speed Circuits

Ahadi, Majid; Roy, Sourajeet

doi:10.1109/tcad.2016.2527711

Cited by 65 publications

(25 citation statements)

References 40 publications

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“…, it can be computed via (6) and the argument of the matrix polynomials is readily obtained as M = A 1 / √ 3, without the need for deriving the recursion coefficients of the normalized Legendre polynomials.…”

Section: Numerical Resultsmentioning

confidence: 99%

The relationship between Galerkin and collocation methods in statistical transmission line analysis

Manfredi

Zutter

Ginste

2016

2016 IEEE 25th Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS)

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Abstract-This paper discusses the relationship between two standard methods for the stochastic analysis of linear circuits, namely the stochastic Galerkin method (SGM) and the stochastic collocation method (SCM), based on a multidimensional Gaussian quadrature. It is established that the SCM corresponds to an approximate factorization of the SGM, involving matrix polynomials sharing the same coefficients as the pertinent polynomial chaos basis functions. Under certain assumptions, the two methods coincide. These findings are illustrated by means of a frequency-domain simulation of a transmission line circuit.

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Section: Numerical Resultsmentioning

confidence: 99%

The relationship between Galerkin and collocation methods in statistical transmission line analysis

Manfredi

Zutter

Ginste

2016

2016 IEEE 25th Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS)

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“…An efficient D-optimal approach based on the optimization of a suitable information matrix has been proposed [69]. Moreover, a sparse linear regression method for high-speed circuits based on the modified Fedorov search algorithm is described in [70], which utilizes comparatively few regression nodes for the PC coefficient computation. Linear regression has been used with optimal regression nodes based on D-optimal design for microwave/RF networks in a multi-dimensional UQ framework [71].…”

Section: Pc-based Applications In Electronicsmentioning

confidence: 99%

“…PC-based methods have been successfully adopted for different UQ problems with a relatively small number of random variables, see, for example, [13,22,24,38,47,48,70,74,92]. However, specific limitations and challenges arise in the application of the PC expansion when a high number of random variables is considered [93].…”

Section: High-dimensional Problemsmentioning

confidence: 99%

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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“…Changes of measure have been used successfully to improve sparse recovery [38,39,40]. Algorithms for generating samples with a well-conditioned Vandermonde matrix via subsampling of tensor-product quadrature have also been used for sparse approximation [41] as well as regression, interpolation and low-rank approximation [42,43,44,45].…”

Section: Related Workmentioning

confidence: 99%

Time and Frequency Domain Methods for Basis Selection in Random Linear Dynamical Systems

Jakeman

Pulch

2018

Int. J. UncertaintyQuantification

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Polynomial chaos methods have been extensively used to analyze systems in uncertainty quantification. Furthermore, several approaches exist to determine a low-dimensional approximation (or sparse approximation) for some quantity of interest in a model, where just a few orthogonal basis polynomials are required. We consider linear dynamical systems consisting of ordinary differential equations with random variables. The aim of this paper is to explore methods for producing low-dimensional approximations of the quantity of interest further. We investigate two numerical techniques to compute a low-dimensional representation, which both fit the approximation to a set of samples in the time domain. On the one hand, a frequency domain analysis of a stochastic Galerkin system yields the selection of the basis polynomials. It follows a linear least squares problem. On the other hand, a sparse minimization yields the choice of the basis polynomials by information from the time domain only. An orthogonal matching pursuit produces an approximate solution of the minimization problem. We compare the two approaches using a test example from a mechanical application.

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Sparse Linear Regression (SPLINER) Approach for Efficient Multidimensional Uncertainty Quantification of High-Speed Circuits

Cited by 65 publications

References 40 publications

The relationship between Galerkin and collocation methods in statistical transmission line analysis

The relationship between Galerkin and collocation methods in statistical transmission line analysis

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

Time and Frequency Domain Methods for Basis Selection in Random Linear Dynamical Systems

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