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Gradient-Enhanced Polynomial Chaos Methods for Circuit Simulation

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Scientific Computing in Electrical Engineering

Part of the book series: Mathematics in Industry ((TECMI,volume 28))

Abstract

Uncertainty Quantification (UQ) is an important and emerging topic in electronic design automation (EDA), as parametric uncertainties are a significant concern for the design of integrated circuits. Historically, various sampling methods such as Monte Carlo (MC) and Latin Hypercube Sampling (LHS) have been employed, but these methods can be prohibitively expensive. Polynomial Chaos Expansion (PCE) methods are often proposed as an alternative to sampling. PCE methods have a number of variations, representing tradeoffs. Regression-based PCE methods, for example, can be applied to existing sample sets and don’t require specific quadrature points. However, this comes at the cost of accuracy. In this paper we explore the idea of enhancing regression-based PCE methods using gradient information. The gradient information is provided by an intrusive adjoint sensitivity algorithm embedded in the circuit simulator.

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Acknowledgements

The authors gratefully acknowledge the anonymous reviewers for their careful reading of the manuscript and their valuable suggestions to improve various aspects of this paper.

This work was sponsored by the Laboratory Directed Research and Development (LDRD) Program at Sandia National Laboratories. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

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Authors and Affiliations

  1. Electrical Models and Simulation, Sandia National Laboratories, Albuquerque, NM, USA

    Eric R. Keiter

  2. Optimization and Uncertainty Quantification, Sandia National Laboratories, Albuquerque, NM, USA

    Laura P. Swiler

  3. Component and Systems Analysis, Sandia National Laboratories, Albuquerque, NM, USA

    Ian Z. Wilcox

Authors
  1. Eric R. Keiter
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  2. Laura P. Swiler
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  3. Ian Z. Wilcox
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Corresponding author

Correspondence to Eric R. Keiter .

Editor information

Editors and Affiliations

  1. Institute of Computational Mathematics (NuMa), Johannes Kepler University (JKU), Linz, Austria

    Ulrich Langer

  2. Institute for Electric Drives and Power Electronics, Johannes Kepler University (JKU), Linz, Austria

    Wolfgang Amrhein

  3. Institute of Computational Mathematics (NuMa), Johannes Kepler University (JKU), Linz, Austria

    Walter Zulehner

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Keiter, E.R., Swiler, L.P., Wilcox, I.Z. (2018). Gradient-Enhanced Polynomial Chaos Methods for Circuit Simulation. In: Langer, U., Amrhein, W., Zulehner, W. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry(), vol 28. Springer, Cham. https://doi.org/10.1007/978-3-319-75538-0_6

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