research-article

Enabling Efficient Analog Synthesis by Coupling Sparse Regression and Polynomial Optimization

Authors:

Michael Orshansky,

Constantine CaramanisAuthors Info & Claims

DAC '14: Proceedings of the 51st Annual Design Automation Conference

Pages 1 - 6

https://doi.org/10.1145/2593069.2593131

Published: 01 June 2014 Publication History

Abstract

The challenge of equation-based analog synthesis comes from its dual nature: functions producing good least-square fits to SPICE-generated data are non-convex, hence not amenable to efficient optimization. In this paper, we leverage recent progress on Semidefinite Programming (SDP) relaxations of polynomial (non-convex) optimization. Using a general polynomial allows for much more accurate fitting of SPICE data compared to the more restricted functional forms. Recent SDP techniques for convex relaxations of polynomial optimizations are powerful but alone still insufficient: even for small problems, the resulting relaxations are prohibitively high dimensional.

We harness these new polynomial tools and realize their promise by introducing a novel regression technique that fits non-convex polynomials with a special sparsity structure. We show that the coupled sparse fitting and optimization (CSFO) flow that we introduce allows us to find accurate high-order polynomials while keeping the resulting optimization tractable.

Using established circuits for optimization experiments, we demonstrate that by handling higher-order polynomials we reduce fitting error to 3.6% from 10%, on average. This translates into a dramatic increase in the rate of constraint satisfaction: for a 1% violation threshold, the success rate is increased from 0% to 78%.

References

[1]

A. S. Bandeira, K. Scheinberg, and L. N. Vicente. Computation of sparse low degree interpolating polynomials and their application to derivative-free optimization. Mathematical programming, 2012.

Digital Library

[2]

S. Boyd, T. Lee, et al. Optimal design of a cmos op-amp via geometric programming. TCAD, 2001.

[3]

W. Daems, G. Gielen, and W. Sansen. Simulation-based generation of posynomial performance models for the sizing of analog integrated circuits. TCAD, 2003.

Digital Library

[4]

M. del Mar Hershenson. Design of pipeline analog-to-digital converters via geometric programming. In ICCAD, 2002.

Digital Library

[5]

L. Jacob, G. Obozinski, and J.-P. Vert. Group lasso with overlap and graph lasso. In ICML. ACM, 2009.

Digital Library

[6]

J. Kim, J. Lee, and L. Vandenberghe. Techniques for improving the accuracy of geometric-programming based analog circuit design optimization. In ICCAD, 2004.

Digital Library

[7]

S. Kim, M. Kojima, and H. Waki. Generalized lagrangian duals and sums of squares relaxations of sparse polynomial optimization problems. SIAM Journal on Optimization, 2005.

Digital Library

[8]

M. Krasnicki, R. Phelps, R. A. Rutenbar, and L. R. Carley. Maelstrom: efficient simulation-based synthesis for custom analog cells. In DAC, 1999.

Digital Library

[9]

J. B. Lasserre. Global optimization with polynomials and the problem of moments. SIAM Journal on Optimization, 2001.

Digital Library

[10]

J. B. Lasserre. Convergent sdp-relaxations in polynomial optimization with sparsity. SIAM Journal on Optimization, 2006.

Digital Library

[11]

S.-H. Lui, H.-K. Kwan, and N. Wong. Analog circuit design by nonconvex polynomial optimization: Two design examples. IJCTA, 2010.

Digital Library

[12]

T. McConaghy, P. Palmers, G. Gielen, and M. Steyaert. Simultaneous multi-topology multi-objective sizing across thousands of analog circuit topologies. In DAC, 2007.

Digital Library

[13]

A. Mutapcic, K. Koh, S. Kim, and S. Boyd. Ggplab version 1.00 a matlab toolbox for geometric programming, 2006.

[14]

P. A. Parrilo and B. Sturmfels. Minimizing polynomial functions. DIMACS, 2003.

[15]

A. K. Singh, K. Ragab, M. Lok, C. Caramanis, and M. Orshansky. Predictable equation-based analog optimization based on explicit capture of modeling error statistics. TCAD, 2012.

Digital Library

[16]

J. A. Tropp and A. C. Gilbert. Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans Inf Theory, 2007.

Digital Library

[17]

H. Waki, S. Kim, M. Kojima, M. Muramatsu, and H. Sugimoto. Algorithm 883: Sparsepop---a sparse semidefinite programming relaxation of polynomial optimization problems. TOMS, 2008.

Digital Library

[18]

M. Yuan and Y. Lin. Model selection and estimation in regression with grouped variables. JRSS, 2006.

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Li WBi ZZeng X(2024)High-Dimensional Analog Circuit Sizing via Bayesian Optimization in the Variational Autoencoder Enhanced Latent Space2024 2nd International Symposium of Electronics Design Automation (ISEDA)10.1109/ISEDA62518.2024.10617489(193-197)Online publication date: 10-May-2024
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cover image ACM Other conferences

DAC '14: Proceedings of the 51st Annual Design Automation Conference

June 2014

1249 pages

ISBN:9781450327305

DOI:10.1145/2593069

Copyright © 2014 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]

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

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Association for Computing Machinery

New York, NY, United States

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Published: 01 June 2014

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DAC '14: The 51st Annual Design Automation Conference 2014

June 1 - 5, 2014

CA, San Francisco, USA

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

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Cited By

Ahmadianshalchi ABelakaria SDoppa J(2024)Preference-Aware Constrained Multi-Objective Bayesian OptimizationProceedings of the 7th Joint International Conference on Data Science & Management of Data (11th ACM IKDD CODS and 29th COMAD)10.1145/3632410.3632427(182-191)Online publication date: 4-Jan-2024
https://dl.acm.org/doi/10.1145/3632410.3632427
Li WBi ZZeng X(2024)High-Dimensional Analog Circuit Sizing via Bayesian Optimization in the Variational Autoencoder Enhanced Latent Space2024 2nd International Symposium of Electronics Design Automation (ISEDA)10.1109/ISEDA62518.2024.10617489(193-197)Online publication date: 10-May-2024
https://doi.org/10.1109/ISEDA62518.2024.10617489
Nguyen THoang TZhang LDobre ODuong T(2024)A Survey on Smart Optimisation Techniques for 6G-oriented Integrated Circuits DesignMobile Networks and Applications10.1007/s11036-024-02343-7Online publication date: 16-May-2024
https://doi.org/10.1007/s11036-024-02343-7
Fan SZhang SLiu JCao NGuo XLi JZhang X(2022)Power Converter Circuit Design Automation Using Parallel Monte Carlo Tree SearchACM Transactions on Design Automation of Electronic Systems10.1145/354953828:2(1-33)Online publication date: 24-Dec-2022
https://dl.acm.org/doi/10.1145/3549538
Budak APan DChen HZhu KLiu MAlawieh MZhang SShi WTang X(2022)CAD for Analog/Mixed‐Signal Integrated CircuitsAdvances in Semiconductor Technologies10.1002/9781119869610.ch3(43-60)Online publication date: 30-Sep-2022
https://doi.org/10.1002/9781119869610.ch3
Huang JYang FYan CZhou DZeng X(2021)A Robust Batch Bayesian Optimization for Analog Circuit Synthesis via Local PenalizationProceedings of the 26th Asia and South Pacific Design Automation Conference10.1145/3394885.3431543(146-151)Online publication date: 18-Jan-2021
https://dl.acm.org/doi/10.1145/3394885.3431543
Zhang SYang FZhou DZeng X(2020)An Efficient Asynchronous Batch Bayesian Optimization Approach for Analog Circuit Synthesis2020 57th ACM/IEEE Design Automation Conference (DAC)10.1109/DAC18072.2020.9218592(1-6)Online publication date: Jul-2020
https://doi.org/10.1109/DAC18072.2020.9218592
Alawieh MWilliamson SPan D(2019)Rethinking Sparsity in Performance Modeling for Analog and Mixed Circuits using Spike and Slab ModelsProceedings of the 56th Annual Design Automation Conference 201910.1145/3316781.3317896(1-6)Online publication date: 2-Jun-2019
https://dl.acm.org/doi/10.1145/3316781.3317896
Alawieh MTang XPan DShibuya T(2019)S2-PMProceedings of the 24th Asia and South Pacific Design Automation Conference10.1145/3287624.3287657(268-273)Online publication date: 21-Jan-2019
https://dl.acm.org/doi/10.1145/3287624.3287657
Alawieh MWang FLi X(2017)Efficient Hierarchical Performance Modeling for Integrated Circuits via Bayesian Co-LearningProceedings of the 54th Annual Design Automation Conference 201710.1145/3061639.3062235(1-6)Online publication date: 18-Jun-2017
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