research-article

BLAST: efficient computation of nonlinear delay sensitivities in electronic and biological networks using barycentric Lagrange enabled transient adjoint analysis

Authors:

Jaijeet RoychowdhuryAuthors Info & Claims

DAC '12: Proceedings of the 49th Annual Design Automation Conference

Pages 301 - 310

https://doi.org/10.1145/2228360.2228417

Published: 03 June 2012 Publication History

Abstract

Transient waveform sensitivities are useful in optimization and also provide direct insight into system metrics such as delay. We present a novel method for finding parametric waveform sensitivities that improves upon current transient adjoint methods, which suffer from quadratic complexity, by applying barycentric Lagrange interpolation to reduce computation to near linear in the time-interval of interest. We apply our technique to find sensitivities of a "nonlinear" Elmore-delay like metric in digital logic and biochemical pathway examples. Our technique achieves order-of-magnitude speedups over traditional adjoint and direct sensitivity computation.

References

[1]

F. Acton. Numerical methods that work. Spectrum Series. Mathematical Association of America, 1990.

[2]

E. Andrianantoandro, S. Basu, D. Karig, and R. Weiss. Synthetic biology: new engineering rules for an emerging discipline. Mol Syst Biol, 2:2006, 2006.

[3]

J. Berrut and L. Trefethen. Barycentric lagrange interpolation. SIAM Review, 46(3):501, 2002.

[4]

D. Boning and S. Nassif. Models of process variations in device and interconnect. In Design of High Performance Microprocessor Circuits, chapter 6. IEEE Press, 1999.

[5]

K. Bowman, S. Duvall, and J. Meindl. Impact of die-to-die and within-die parameter fluctuations on the maximum clock frequency distribution for gigascale integration. Solid-State Circuits, IEEE Journal of, 37(2): 183--190, Feb 2002.

[6]

P. Chan and K. Karplus. Computing signal delay in general re networks by tree/link partitioning. Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on, 9(8):898--902, Aug 1990.

Digital Library

[7]

W. Cheney and D. Kincaid. Numerical Mathematics and Computing. Brooks/Cole, Pacific Grove, CA, 3d edition, 1994.

Digital Library

[8]

A. Conn, I. Elfadel, J. Molzen, W. W., P. O'Brien, P. Strenski, C. Visweswariah, and C. Whan. Gradient-based optimization of custom circuits using a static-timing formulation. In Design Automation Conference, 1999. Proceedings. 36th, pages 452--459, 1999.

Digital Library

[9]

S. Director and R. Rohrer. The Generalized Adjoint Network and Network Sensitivities. IEEE Trans. Ckt. Theory, 16:318--323, August 1969.

[10]

W. C. Elmore. The transient response of damped linear networks with particular regard to wideband amplifiers. Journal of Applied Physics, 19(1):55--63, Jan 1948.

[11]

P. Feldmann, T. Nguyen, S. Director, and R. Rohrer. Sensitivity computation in piecewise approximate circuit simulation. Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on, 10(2):171--183, feb 1991.

Digital Library

[12]

A. Griewank. On automatic differentiation. Mathematical Programming: recent developments and applications, pages 83--108, 1989.

[13]

R. Hitchcock, G. Smith, D. Cheng, et al. Timing analysis of computer hardware. IBM Journal of Research and Development, 26(1):100--105, Jan 1982.

Digital Library

[14]

D. Hocevar, P. Yang, T. Trick, and B. Epler. Transient sensitivity computation for mosfet circuits. IEEE Trans, on CAD of Integrated Circuits and Systems, 4(4):609, 1985.

Digital Library

[15]

K. Hoffman and R. Kunze. Linear algebra. Prentice-Hall mathematics series. Prentice-Hall, 1971.

[16]

S. Hooshangi, S. Thiberge, and R. Weiss. Ultrasensitivity and noise propagation in a synthetic transcriptional cascade. Proc Natl Acad Sci USA, 102(10):3581--3586, Mar. 2005.

[17]

Z. Ilievski, H. Xu, A. Verhoeven, E. Maten, W. Schilders, and R. Mattheij. Adjoint transient sensitivity analysis in circuit simulation. Scientific Computing in Electrical Engineering, 2006.

[18]

T. Lin and C. Mead. Signal delay in general re networks. Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on, 3(4):331--349, October 1984.

Digital Library

[19]

N. Menezes, R. Baldick, and L. Pileggi. A sequential quadratic programming approach to concurrent gate and wire sizing. Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on, 16(8):867--881, Aug 1997.

Digital Library

[20]

N. Menezes, S. Pullela, F. Dartu, and L. Pillage. Re interconnect synthesis-a moment fitting approach. In Computer-Aided Design, 1994., IEEE/ACM International Conference on, pages 418--425, Nov 1994.

Digital Library

[21]

S. Nazarian, M. Pedram, E. Tuncer, and T. Lin. Sensitivity-based gate delay propagation in static timing analysis. In Quality of Electronic Design, 2005. ISQED 2005. Sixth International Symposium on, pages 536--541, March 2005.

Digital Library

[22]

R. Neidinger. Introduction to Automatic Differentiation and MATLAB Object-Oriented Programming. SIAM Review, 52(3):545--563, 2010.

Digital Library

[23]

A. Odabasioglu, M. Celik, and L. Pileggi. Prima: passive reduced-order interconnect macromodeling algorithm. Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on, 17(8):645--654, Aug 1998.

Digital Library

[24]

J. Ousterhout. Crystal: A timing analyzer for nmos vlsi circuits. Technical Report UCB/CSD-83-119, EECS Department, University of California, Berkeley, Jan 1983.

Digital Library

[25]

L. Pillage and R. Rohrer. Asymptotic waveform evaluation for timing analysis. Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on, 9(4):352--366, Apr 1990.

Digital Library

[26]

P. Purnick and R. Weiss. The second wave of synthetic biology: from modules to systems. Nature Reviews Molecular Cell Biology, 10(6):410--422, 2009.

[27]

J. Roychowdhury. Numerical simulation and modelling of electronic and biochemical systems. Foundations and Trends in Electronic Design Automation, 3(2--3):97--303, 2009.

Digital Library

[28]

H. Rutishauser. Vorlesungen her numerische Mathematik. Birkhuser-Verlag, 1976.

Cited By

Hu WYin SWang LLiu CWang ZYe ZWang Y(2023)An Early-Stop Adjoint Transient Sensitivity Analysis Method for Objective Functions Associated with Many Time PointsTsinghua Science and Technology10.26599/TST.2022.901002428:3(566-579)Online publication date: Jun-2023
https://doi.org/10.26599/TST.2022.9010024
Sagan NRoychowdhury JWang T(2022)Transient Adjoint DAE Sensitivities: A Complete, Rigorous, and Numerically Accurate FormulationProceedings of the 27th Asia and South Pacific Design Automation Conference10.1109/ASP-DAC52403.2022.9712537(513-518)Online publication date: 17-Jan-2022
https://dl.acm.org/doi/10.1109/ASP-DAC52403.2022.9712537
Hu WYe ZWang Y(2020)Adjoint Transient Sensitivity Analysis for Objective Functions Associated to Many Time Points2020 57th ACM/IEEE Design Automation Conference (DAC)10.1109/DAC18072.2020.9218602(1-6)Online publication date: Jul-2020
https://doi.org/10.1109/DAC18072.2020.9218602
Show More Cited By

Index Terms

BLAST: efficient computation of nonlinear delay sensitivities in electronic and biological networks using barycentric Lagrange enabled transient adjoint analysis
1. Hardware
  1. Hardware validation

Recommendations

A Projection-Based Reduction Approach to Computing Sensitivity of Steady-State Response of Nonlinear Circuits

This paper presents a new algorithm for computing the sensitivity of steady-state responses of nonlinear circuits with respect to an arbitrary network parameter. The proposed algorithm is based on circuit-reduction techniques obtained through nonlinear-...
Monte Carlo algorithms for evaluating Sobol' sensitivity indices

Sensitivity analysis is a powerful technique used to determine robustness, reliability and efficiency of a model. The main problem in this procedure is the evaluating total sensitivity indices that measure a parameter's main effect and all the ...
Fast, non-Monte-Carlo estimation of transient performance variation due to device mismatch

This paper describes an efficient way of simulating the effects of device random mismatch on circuit transient characteristics, such as variations in delay or in frequency. The proposed method models DC random offsets as equivalent AC pseudonoises and ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

DAC '12: Proceedings of the 49th Annual Design Automation Conference

June 2012

1357 pages

ISBN:9781450311991

DOI:10.1145/2228360

General Chair:
Patrick Groeneveld
Magma Design Automation, Inc., San Jose, CA
,
Program Chairs:
Donatella Sciuto
Politecnico di Milano, Milano, Italy
,
Soha Hassoun
Tufts Univ., Medford, MA

Copyright © 2012 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

EDAC: Electronic Design Automation Consortium
SIGDA: ACM Special Interest Group on Design Automation
IEEE-CEDA

In-Cooperation

SIGBED: ACM Special Interest Group on Embedded Systems

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 03 June 2012

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

DAC '12

Sponsor:

EDAC
SIGDA

DAC '12: The 49th Annual Design Automation Conference 2012

June 3 - 7, 2012

California, San Francisco

Acceptance Rates

Overall Acceptance Rate 1,770 of 5,499 submissions, 32%

Upcoming Conference

DAC '25

Sponsor:
sigda

62nd ACM/IEEE Design Automation Conference

June 22 - 26, 2025

San Francisco , CA , USA

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

7
Total Citations
View Citations
137
Total Downloads

Downloads (Last 12 months)7
Downloads (Last 6 weeks)1

Reflects downloads up to 08 Mar 2025

Other Metrics

View Author Metrics

Citations

Cited By

Hu WYin SWang LLiu CWang ZYe ZWang Y(2023)An Early-Stop Adjoint Transient Sensitivity Analysis Method for Objective Functions Associated with Many Time PointsTsinghua Science and Technology10.26599/TST.2022.901002428:3(566-579)Online publication date: Jun-2023
https://doi.org/10.26599/TST.2022.9010024
Sagan NRoychowdhury JWang T(2022)Transient Adjoint DAE Sensitivities: A Complete, Rigorous, and Numerically Accurate FormulationProceedings of the 27th Asia and South Pacific Design Automation Conference10.1109/ASP-DAC52403.2022.9712537(513-518)Online publication date: 17-Jan-2022
https://dl.acm.org/doi/10.1109/ASP-DAC52403.2022.9712537
Hu WYe ZWang Y(2020)Adjoint Transient Sensitivity Analysis for Objective Functions Associated to Many Time Points2020 57th ACM/IEEE Design Automation Conference (DAC)10.1109/DAC18072.2020.9218602(1-6)Online publication date: Jul-2020
https://doi.org/10.1109/DAC18072.2020.9218602
Keiter ESwiler LWilcox I(2018)Gradient-Enhanced Polynomial Chaos Methods for Circuit SimulationScientific Computing in Electrical Engineering10.1007/978-3-319-75538-0_6(55-68)Online publication date: 14-Apr-2018
https://doi.org/10.1007/978-3-319-75538-0_6
Aadithya KKeiter EMei TParameswaran S(2017)DAGSENSProceedings of the 36th International Conference on Computer-Aided Design10.5555/3199700.3199721(155-162)Online publication date: 13-Nov-2017
https://dl.acm.org/doi/10.5555/3199700.3199721
Aadithya KKeiter EMei T(2017)DAGSENS: Directed acyclic graph based direct and adjoint transient sensitivity analysis for event-driven objective functions2017 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)10.1109/ICCAD.2017.8203773(155-162)Online publication date: Nov-2017
https://doi.org/10.1109/ICCAD.2017.8203773
Liu FFeldmann P(2014)A Time-Unrolling Method to Compute Sensitivity of Dynamic SystemsProceedings of the 51st Annual Design Automation Conference10.1145/2593069.2593080(1-6)Online publication date: 1-Jun-2014
https://dl.acm.org/doi/10.1145/2593069.2593080

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Table of Conten