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 . 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.
@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 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/ 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://msia.centre-mersenne.org/articles/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] 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] Importance sampling for jump processes and applications to finance, J. Comput. Finance, Volume 2 (2015) no. 19
[3] 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] Adaptive Optimal Allocation in Stratified Sampling Methods, Methodol. Comput. Appl. Probab., Volume 12 (2010) no. 3, pp. 335-360 | DOI | MR | Zbl
[5] 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] Variability in Scaled MOSFETs, Nanoscale Silicon Devices (2015) | DOI
[7] The modified nodal approach to network analysis, IEEE Trans. Circuits Syst., Volume 22 (1975) no. 6, pp. 504-509 | DOI
[8] 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] Robust Adaptive Importance Sampling for Normal Random Vectors, Ann. Appl. Probab., Volume 19 (2009) no. 5, pp. 1687-1718 | MR | Zbl
[10] 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] 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] Probability in Banach spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., 23, Springer, 1991 | DOI
[13] Fundamentals of Computer-Aided Circuit Simulation, Kluwer Academic Publishers, 1987 | DOI
[14] Variation-Aware Design of Custom Integrated Circuits: A Hands-on Field Guide, Springer, 2013, pp. 187-188 | DOI
[15] Discrete event systems, Wiley Series in Probability and Mathematical Statistics: Probability and mathematical statistics, John Wiley & Sons, 1993
[16] 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] Computer Methods for Circuit Analysis and Design, John Wiley & Sons, 1993
Cited by Sources: