Stochastic Interpolation Model Scheme and Its Application to Statistical Circuit Analysis

Jin-Qin LU; Kimihiro OGAWA; Masayuki TAKAHASHI; Takehiko ADACHI

Stochastic Interpolation Model Scheme and Its Application to Statistical Circuit Analysis

Jin-Qin LU, Kimihiro OGAWA, Masayuki TAKAHASHI, Takehiko ADACHI

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IC performance simulation for statistical purpose is usually very time-consuming since the scale and complexity of IC have increased greatly in recent years. A common approach for reduction of simulation cost is aimed at the nature of simple modeling instead of actual circuit performance simulations. In this paper,a stochastic interpolation model (SIM) scheme is proposed which overcomes the drawbacks of the existing polynomial-based approximation schemes. First,the dependence of the R²_press statistic upon a parameter in SIM is taken into account and by maximizing R²_press this enables SIM to achieve the best approximation accuracy in the given sample points without any assumption on the sample data. Next, a sequential sampling strategy based on variance analysis is described to effectively construct SIM during its update process. In each update step, a new sample point with a maximal value of variance is added to the former set of the sample points. The update process will be continued until the desired approximation accuracy is reached. This would eventually lead to the realization of SIM with a quite small number of sample points. Finally, the coefficient of variance is introduced as another criterion for approximation accuracy check other than the R²_press statistic. The effectiveness of presented implementation scheme is demonstrated by several numerical examples as well as a statistical circuit analysis example.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E77-A No.3 pp.447-453

Publication Date: 1994/03/25

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Type of Manuscript: Special Section PAPER (Special Section on the 6th Karuizawa Workshop on Circuits and Systems)

Category: Modeling and Simulation

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Jin-Qin LU, Kimihiro OGAWA, Masayuki TAKAHASHI, Takehiko ADACHI, "Stochastic Interpolation Model Scheme and Its Application to Statistical Circuit Analysis" in IEICE TRANSACTIONS on Fundamentals, vol. E77-A, no. 3, pp. 447-453, March 1994, doi: .
Abstract: IC performance simulation for statistical purpose is usually very time-consuming since the scale and complexity of IC have increased greatly in recent years. A common approach for reduction of simulation cost is aimed at the nature of simple modeling instead of actual circuit performance simulations. In this paper,a stochastic interpolation model (SIM) scheme is proposed which overcomes the drawbacks of the existing polynomial-based approximation schemes. First,the dependence of the R²_press statistic upon a parameter in SIM is taken into account and by maximizing R²_press this enables SIM to achieve the best approximation accuracy in the given sample points without any assumption on the sample data. Next, a sequential sampling strategy based on variance analysis is described to effectively construct SIM during its update process. In each update step, a new sample point with a maximal value of variance is added to the former set of the sample points. The update process will be continued until the desired approximation accuracy is reached. This would eventually lead to the realization of SIM with a quite small number of sample points. Finally, the coefficient of variance is introduced as another criterion for approximation accuracy check other than the R²_press statistic. The effectiveness of presented implementation scheme is demonstrated by several numerical examples as well as a statistical circuit analysis example.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e77-a_3_447/_p

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@ARTICLE{e77-a_3_447,
author={Jin-Qin LU, Kimihiro OGAWA, Masayuki TAKAHASHI, Takehiko ADACHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Stochastic Interpolation Model Scheme and Its Application to Statistical Circuit Analysis},
year={1994},
volume={E77-A},
number={3},
pages={447-453},
abstract={IC performance simulation for statistical purpose is usually very time-consuming since the scale and complexity of IC have increased greatly in recent years. A common approach for reduction of simulation cost is aimed at the nature of simple modeling instead of actual circuit performance simulations. In this paper,a stochastic interpolation model (SIM) scheme is proposed which overcomes the drawbacks of the existing polynomial-based approximation schemes. First,the dependence of the R²_press statistic upon a parameter in SIM is taken into account and by maximizing R²_press this enables SIM to achieve the best approximation accuracy in the given sample points without any assumption on the sample data. Next, a sequential sampling strategy based on variance analysis is described to effectively construct SIM during its update process. In each update step, a new sample point with a maximal value of variance is added to the former set of the sample points. The update process will be continued until the desired approximation accuracy is reached. This would eventually lead to the realization of SIM with a quite small number of sample points. Finally, the coefficient of variance is introduced as another criterion for approximation accuracy check other than the R²_press statistic. The effectiveness of presented implementation scheme is demonstrated by several numerical examples as well as a statistical circuit analysis example.},
keywords={},
doi={},
ISSN={},
month={March},}

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TY - JOUR
TI - Stochastic Interpolation Model Scheme and Its Application to Statistical Circuit Analysis
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 447
EP - 453
AU - Jin-Qin LU
AU - Kimihiro OGAWA
AU - Masayuki TAKAHASHI
AU - Takehiko ADACHI
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E77-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 1994
AB - IC performance simulation for statistical purpose is usually very time-consuming since the scale and complexity of IC have increased greatly in recent years. A common approach for reduction of simulation cost is aimed at the nature of simple modeling instead of actual circuit performance simulations. In this paper,a stochastic interpolation model (SIM) scheme is proposed which overcomes the drawbacks of the existing polynomial-based approximation schemes. First,the dependence of the R²_press statistic upon a parameter in SIM is taken into account and by maximizing R²_press this enables SIM to achieve the best approximation accuracy in the given sample points without any assumption on the sample data. Next, a sequential sampling strategy based on variance analysis is described to effectively construct SIM during its update process. In each update step, a new sample point with a maximal value of variance is added to the former set of the sample points. The update process will be continued until the desired approximation accuracy is reached. This would eventually lead to the realization of SIM with a quite small number of sample points. Finally, the coefficient of variance is introduced as another criterion for approximation accuracy check other than the R²_press statistic. The effectiveness of presented implementation scheme is demonstrated by several numerical examples as well as a statistical circuit analysis example.
ER -