Skip to main content

Machine Learning-Based System Optimization and Uncertainty Quantification for Integrated Systems

  • Chapter
  • First Online:
Machine Learning in VLSI Computer-Aided Design

Abstract

Increasing complexity and higher integration of electronics leads to new challenges in system optimization. This is because modern systems contain structures with multi-scale geometries whose responses are determined by multi-physics simulations and often times contain components that are electromagnetically coupled. In practice, the use of optimization algorithms in the design cycle of such systems is limited to fine-tuning an already good design, which requires substantial human intervention and CPU time to arrive at an optimum solution. This is mainly due to lack of methods capable of handling high dimensionality at the same time converging to the global optimum regardless of the initial point selection. We therefore present a new, EDA oriented method, utilizing machine learning techniques to perform black-box optimization that starts with zero training data and ensures convergence to global optimum in the minimum amount of CPU time. In order to consider uncertainties in fabrication that are likely to cause deviations in the final design from the optimal design parameters, we present a ML-based uncertainty quantification (UQ) methodology. Although the combination of optimization and UQ algorithms presented in this chapter are fully automated and generic, we demonstrate these methods on an emerging application in system integration and power delivery, namely integrated voltage regulators (IVR). The IVR considered here is based on system in package (SiP) technology.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. N. Sturcken, E.J. O’Sullivan, N. Wang, P. Herget, B.C. Webb, L.T. Romankiw, M. Petracca, R. Davies, R.E. Fontana, G.M. Decad, I. Kymissis, A.V. Peterchev, L.P. Carloni, W.J. Gallagher, K.L. Shepard, A 2.5d integrated voltage regulator using coupled-magnetic-core inductors on silicon interposer. IEEE J. Solid-State Circuits 48(1), 244–254 (2013)

    Google Scholar 

  2. N. Sturcken, M. Petracca, S. Warren, P. Mantovani, L.P. Carloni, A.V. Peterchev, K.L. Shepard, A switched-inductor integrated voltage regulator with nonlinear feedback and network-on-chip load in 45 nm SOI. IEEE J. Solid-State Circuits 47(8), 1935–1945 (2012)

    Article  Google Scholar 

  3. S. Mueller, K.Z. Ahmed, A. Singh, A.K. Davis, S. Mukhopadyay, M. Swaminathan, Y. Mano, Y. Wang, J. Wong, S. Bharathi, H.F. Moghadam, D. Draper, Design of high efficiency integrated voltage regulators with embedded magnetic core inductors, in 2016 IEEE 66th Electronic Components and Technology Conference (ECTC) (2016), pp. 566–573

    Google Scholar 

  4. H.M. Torun, M. Swaminathan, Black box optimization of 3D integrated systems, in Computational Modelling of Multi Uncertainty and Multi-Scale Problems (COMUS) (2017)

    Google Scholar 

  5. H.M. Torun, M. Swaminathan, A.K. Davis, M.L.F. Bellaredj, A global Bayesian optimization algorithm and its application to integrated system design. IEEE Trans. Very Large Scale Integr. VLSI Syst. 26(4), 792–802 (2018)

    Article  Google Scholar 

  6. H.M. Torun, M. Swaminathan, Black box optimization of 3D integrated systems using machine learning, in 2017 IEEE 26th Conference on Electrical Performance of Electronic Packaging and Systems, EPEPS (2017)

    Google Scholar 

  7. H.M. Torun, C.A. Pardue, M.L.F. Belladredj, A.K. Davis, M. Swaminathan, Machine learning driven advanced packaging and system miniaturization of IoT for wireless power transfer solutions, in IEEE 68th Electronic Components Technology Conference, ECTC (2018)

    Google Scholar 

  8. H.M. Torun, M. Larbi, M. Swaminathan, A bayesian framework for optimizing interconnects in High-Speed channels, in 2018 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO2018), Reykjavik, Iceland (2018)

    Google Scholar 

  9. G. Blatman, B. Sudret, Adaptive sparse polynomial chaos expansion based on least angle regression. J. Comput. Phys. 230(6), 2345–2367 (2011)

    Article  MathSciNet  Google Scholar 

  10. M. Larbi, I.S. Stievano, F.G. Canavero, P. Besnier, Variability impact of many design parameters: the case of a realistic electronic link. IEEE Trans. Electromagn. Compat. 60(1), 34–41 (2018). https://doi.org/10.1109/TEMC.2017.2727961

    Article  Google Scholar 

  11. S.J. Park, B. Bae, J. Kim, M. Swaminathan, Application of machine learning for optimization of 3-D integrated circuits and systems. IEEE Trans. Very Large Scale Integr. VLSI Syst. 25(6), 1856–1865 (2017)

    Article  Google Scholar 

  12. K. Kawaguchi, L.P. Kaelbling, T. Lozano-Pérez, Bayesian optimization with exponential convergence. Adv. Neural Inf. Process. Syst. 2809–2817 (2015)

    Google Scholar 

  13. E. Brochu, V.M. Cora, N. de Freitas, A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. arXiv.org, arXiv:1012.2599 (2010)

    Google Scholar 

  14. N. Srinivas, A. Krause, S.M. Kakade, M. Seeger, Gaussian process optimization in the bandit setting: no regret and experimental design. arXiv:0912.3995 (2009)

    Google Scholar 

  15. J.R. Gardner, M.J. Kusner, Z.E. Xu, K.Q. Weinberger, J.P. Cunningham, Bayesian optimization with inequality constraints, in Proceedings of the 31st International Conference on Machine Learning, ICML (2014), pp. 937–945

    Google Scholar 

  16. Z. Wang, B. Shakibi, L. Jin, N. Freitas, Bayesian multi-scale optimistic optimization, in Artificial Intelligence and Statistics (2014), pp. 1005–1014

    Google Scholar 

  17. R. Munos, Optimistic optimization of a deterministic function without the knowledge of its smoothness, in Advances in Neural Information Processing Systems (2011), pp. 783–791

    Google Scholar 

  18. M.D. Hoffman, E. Brochu, N. de Freitas, Portfolio allocation for Bayesian optimization. in Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence, UAI (2011), pp. 327–336

    Google Scholar 

  19. S. Surjanovic, Virtual library of simulation experiments [Online]. https://www.sfu.ca/~ssurjano/

  20. D.J. Lizotte, Practical bayesian optimization. Ph.D Thesis, University of Alberta, 2008

    Google Scholar 

  21. D.R. Jones, A taxonomy of global optimization methods based on response surfaces. J. Glob. Optim. 21(4), 345–383 (2001)

    Article  MathSciNet  Google Scholar 

  22. ANSYS, Ansys HFSS ver. 2015.2 [Online]. http://www.ansys.com

  23. ANSYS, Ansys Maxwell ver. 2015.2 [Online]. http://www.ansys.com

  24. D.S. Gardner, G. Schrom, F. Paillet, B. Jamieson, T. Karnik, S. Borkar, Review of on-chip inductor structures with magnetic films. IEEE Trans. Magn. 45(10), 4760–4766 (2009)

    Article  Google Scholar 

  25. M.L.F. Bellaredj, S. Mueller, A.K. Davis, P. Kohl, M. Swaminathan, Y. Mano, Fabrication, characterization and comparison of fr4-compatible composite magnetic materials for high efficiency integrated voltage regulators with embedded magnetic core micro-inductors, in 2017 IEEE 67th Electronic Components and Technology Conference (ECTC) (2017)

    Google Scholar 

  26. M. Swaminathan, Power delivery for electronic system consortium (PDES). Georgia Institute of Technology (2017)

    Google Scholar 

  27. A. Rong, A.C. Cangellaris, Interconnect transient simulation in the presence of layout and routing uncertainty, in 2011 IEEE 20th Conference on Electrical Performance of Electronic Packaging and Systems (2011), pp. 157–160

    Google Scholar 

  28. A.K. Prasad, M. Ahadi, B.S. Thakur, S. Roy, Accurate polynomial chaos expansion for variability analysis using optimal design of experiments, in 2015 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO) (2015), pp. 1–4

    Google Scholar 

  29. D.V. Ginste, D.D. Zutter, D. Deschrijver, T. Dhaene, P. Manfredi, F. Canavero, Stochastic modeling-based variability analysis of on-chip interconnects. IEEE Trans. Compon. Packag. Manuf. Technol. 2(7), 1182–1192 (2012)

    Article  Google Scholar 

  30. B. Sudret, Uncertainty propagation and sensitivity analysis in mechanical models–contributions to structural reliability and stochastic spectral methods. Habilitation à diriger des recherches, Université Blaise Pascal, Clermont-Ferrand, 2007

    Google Scholar 

  31. Z. Zhang, T.W. Weng, L. Daniel, Big-data tensor recovery for high-dimensional uncertainty quantification of process variations. IEEE Trans. Compon. Packag. Manuf. Technol. 7(5), 687–697 (2017)

    Article  Google Scholar 

  32. A.K. Prasad, S. Roy, Accurate reduced dimensional polynomial chaos for efficient uncertainty quantification of microwave/RF networks. IEEE Trans. Microwave Theory Tech. (2017). https://doi.org/10.1109/TMTT.2017.2689742

  33. C. Soize, R. Ghanem, Physical systems with random uncertainties: chaos representations with arbitrary probability measure. SIAM J. Sci. Comput. 26(2), 395–410 (2004)

    Article  MathSciNet  Google Scholar 

  34. M. Berveiller, B. Sudret, M. Lemaire, Stochastic finite element: a non intrusive approach by regression. Eur. J. Comput. Mech. 15(1–3), 81–92 (2006)

    Article  Google Scholar 

  35. D.C. Montgomery, Design and Analysis of Experiments (Wiley, New York, 2004)

    Google Scholar 

  36. B. Efron, T. Hastie, I. Johnstone, R. Tibshirani, Least angle regression. Ann. Stat. 32(2), 407–499 (2004)

    Article  MathSciNet  Google Scholar 

  37. I.M. Sobol, Sensitivity estimates for nonlinear mathematical models. Math. Model. Comput. Exp. 1(4), 407–414 (1993)

    MathSciNet  MATH  Google Scholar 

  38. B. Sudret, Global sensitivity analysis using polynomial chaos expansions. Reliab. Eng. Syst. Saf. 93(7), 964–979 (2008)

    Article  Google Scholar 

  39. M.D. McKay, R.J. Beckman, W.J. Conover, A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 42(1), 55–61 (2000)

    Article  Google Scholar 

  40. S. Marelli, B. Sudret, UQLab: a framework for uncertainty quantification in matlab, in Proceedings of 2nd International Conference on Vulnerability Risk Analysis and Management, Liverpool (2014), pp. 2554–2563

    Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Science Foundation under Grant No. CNS 16-24810—Center for Advanced Electronics through Machine Learning (CAEML) and Power Delivery for Electronic Systems (PDES) Consortium, Georgia Tech, USA. The authors would also like to acknowledge Dr. Mohamed L. F. Bellaredj, Dr. Anto K. Davis, and Dr. Colin Pardue for their assistance in simulation and analysis of the IVR.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Madhavan Swaminathan .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Torun, H.M., Larbi, M., Swaminathan, M. (2019). Machine Learning-Based System Optimization and Uncertainty Quantification for Integrated Systems. In: Elfadel, I., Boning, D., Li, X. (eds) Machine Learning in VLSI Computer-Aided Design. Springer, Cham. https://doi.org/10.1007/978-3-030-04666-8_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-04666-8_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04665-1

  • Online ISBN: 978-3-030-04666-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics