Rare event simulation for electronic circuit design
MathematicS In Action, Volume 11 (2022) no. 1, pp. 91-108.

In this work, we propose an algorithm to simulate rare events for electronic circuit design. Our approach heavily relies on a smart use of importance sampling, which enables us to tackle probabilities of the magnitude ${10}^{-10}$. Not only can we compute very rare default probability, but we can also compute the quantile associated to a given default probability and its expected shortfall. We show the impressive efficiency of the method on real circuits.

Published online:
DOI: 10.5802/msia.19
Xavier Jonsson 1; Jérôme Lelong 2

1 Siemens Electronic Design Automation, 110 Rue Blaise Pascal, 38330 Montbonnot France
2 Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK, 38000 Grenoble, France
Copyrights: The authors retain unrestricted copyrights and publishing rights
@article{MSIA_2022__11_1_91_0,
author = {Xavier Jonsson and J\'er\^ome Lelong},
title = {Rare event simulation for electronic circuit design},
journal = {MathematicS In Action},
pages = {91--108},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {11},
number = {1},
year = {2022},
doi = {10.5802/msia.19},
language = {en},
url = {https://msia.centre-mersenne.org/articles/10.5802/msia.19/}
}
TY  - JOUR
AU  - Xavier Jonsson
AU  - Jérôme Lelong
TI  - Rare event simulation for electronic circuit design
JO  - MathematicS In Action
PY  - 2022
DA  - 2022///
SP  - 91
EP  - 108
VL  - 11
IS  - 1
PB  - Société de Mathématiques Appliquées et Industrielles
UR  - https://msia.centre-mersenne.org/articles/10.5802/msia.19/
UR  - https://doi.org/10.5802/msia.19
DO  - 10.5802/msia.19
LA  - en
ID  - MSIA_2022__11_1_91_0
ER  -
%0 Journal Article
%A Xavier Jonsson
%A Jérôme Lelong
%T Rare event simulation for electronic circuit design
%J MathematicS In Action
%D 2022
%P 91-108
%V 11
%N 1
%I Société de Mathématiques Appliquées et Industrielles
%U https://doi.org/10.5802/msia.19
%R 10.5802/msia.19
%G en
%F MSIA_2022__11_1_91_0
Xavier Jonsson; Jérôme Lelong. Rare event simulation for electronic circuit design. MathematicS In Action, Volume 11 (2022) no. 1, pp. 91-108. doi : 10.5802/msia.19. https://msia.centre-mersenne.org/articles/10.5802/msia.19/

[1] Kanak Agarwal; Sani Nassif The Impact of Random Device Variation on SRAM Cell Stability in Sub-90-nm CMOS Technologies, IEEE Trans. VLSI Syst., Volume 16 (2008) no. 1, pp. 86-97 | DOI

[2] Laetitia Badouraly Kassim; Jérôme Lelong; Imane Loumrhari Importance sampling for jump processes and applications to finance, J. Comput. Finance, Volume 2 (2015) no. 19

[3] J. Craninckx; M. S. J. Steyaert A 1.8-GHz low-phase-noise CMOS VCO using optimized hollow spiral inductors, IEEE J. Solid-State Circuits, Volume 32 (1997) no. 5, pp. 736-744 | DOI

[4] Pierre Etoré; Benjamin Jourdain Adaptive Optimal Allocation in Stratified Sampling Methods, Methodol. Comput. Appl. Probab., Volume 12 (2010) no. 3, pp. 335-360 | DOI | MR | Zbl

[5] Paul Glasserman; Philip Heidelberger; Perwez Shahabuddin Asymptotically optimal importance sampling and stratification for pricing path-dependent options, Math. Finance, Volume 9 (1999) no. 2, pp. 117-152 | DOI | MR | Zbl

[6] T. Hiramoto Variability in Scaled MOSFETs, Nanoscale Silicon Devices (2015) | DOI

[7] Chung-Wen Ho; A. Ruehli; P. Brennan The modified nodal approach to network analysis, IEEE Trans. Circuits Syst., Volume 22 (1975) no. 6, pp. 504-509 | DOI

[8] D. E. Hocevar; M. R. Lightner; T. N. Trick A Study of Variance Reduction Techniques for Estimating Circuit Yields, IEEE Trans. CAD Integr. Circuits Syst., Volume 2 (1983) no. 3, pp. 180-192 | DOI

[9] Benjamin Jourdain; Jérôme Lelong Robust Adaptive Importance Sampling for Normal Random Vectors, Ann. Appl. Probab., Volume 19 (2009) no. 5, pp. 1687-1718 | MR | Zbl

[10] R. Kanj; R. Joshi; S. Nassif Mixture importance sampling and its application to the analysis of SRAM designs in the presence of rare failure events, 2006 43rd ACM/IEEE Design Automation Conference (2006), pp. 69-72 | DOI

[11] Dirk P. Kroese; Sergey Porotsky; Reuven Y. Rubinstein The cross-entropy method for continuous multi-extremal optimization, Methodol. Comput. Appl. Probab., Volume 8 (2006) no. 3, pp. 383-407 | DOI | MR | Zbl

[12] Michel Ledoux; Michel Talagrand Probability in Banach spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., 23, Springer, 1991 | DOI

[13] William J. McCalla Fundamentals of Computer-Aided Circuit Simulation, Kluwer Academic Publishers, 1987 | DOI

[14] Trent McConaghy; Kristopher Breen; Jeffrey Dyck; Amit Gupta Variation-Aware Design of Custom Integrated Circuits: A Hands-on Field Guide, Springer, 2013, pp. 187-188 | DOI

[15] Reuven Y. Rubinstein; Alexander Shapiro Discrete event systems, Wiley Series in Probability and Mathematical Statistics: Probability and mathematical statistics, John Wiley & Sons, 1993

[16] Amith Singhee; Rob A. Rutenbar Statistical Blockade: Very Fast Statistical Simulation and Modeling of Rare Circuit Events and Its Application to Memory Design, IEEE Trans. CAD Integr. Circuits Syst., Volume 28 (2009) no. 8, pp. 1176-1189 | DOI

[17] Jiérâi Vlach; Kishore Singhal Computer Methods for Circuit Analysis and Design, John Wiley & Sons, 1993

Cited by Sources: