Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification
Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadr...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2017
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| Online Access: | http://hdl.handle.net/1721.1/108269 https://orcid.org/0000-0002-5880-3151 |
| _version_ | 1826198006331867136 |
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| author | El-Moselhy, Tarek A. Elfadel, Ibrahim M. Zhang, Zheng Daniel, Luca |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science El-Moselhy, Tarek A. Elfadel, Ibrahim M. Zhang, Zheng Daniel, Luca |
| author_sort | El-Moselhy, Tarek A. |
| collection | MIT |
| description | Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input a-priori. However, individual system components are often described by surrogate models rather than density functions. In order to apply stochastic spectral methods in hierarchical uncertainty quantification, we first propose to construct physically consistent closed-form density functions by two monotone interpolation schemes. Then, by exploiting the special forms of the obtained density functions, we determine the generalized polynomial-chaos basis functions and the Gauss quadrature rules that are required by a stochastic spectral simulator. The effectiveness of our proposed algorithm is verified by both synthetic and practical circuit examples. |
| first_indexed | 2024-09-23T10:57:24Z |
| format | Article |
| id | mit-1721.1/108269 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:57:24Z |
| publishDate | 2017 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1082692022-09-27T16:10:32Z Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification El-Moselhy, Tarek A. Elfadel, Ibrahim M. Zhang, Zheng Daniel, Luca Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Research Laboratory of Electronics Daniel, Luca Zhang, Zheng Daniel, Luca Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input a-priori. However, individual system components are often described by surrogate models rather than density functions. In order to apply stochastic spectral methods in hierarchical uncertainty quantification, we first propose to construct physically consistent closed-form density functions by two monotone interpolation schemes. Then, by exploiting the special forms of the obtained density functions, we determine the generalized polynomial-chaos basis functions and the Gauss quadrature rules that are required by a stochastic spectral simulator. The effectiveness of our proposed algorithm is verified by both synthetic and practical circuit examples. Massachusetts Institute of Technology-Skolkovo Institute of Science and Technology program MIT & Masdar Institute Cooperative Program 2017-04-19T19:16:12Z 2017-04-19T19:16:12Z 2014-04 Article http://purl.org/eprint/type/JournalArticle 0278-0070 1937-4151 http://hdl.handle.net/1721.1/108269 Zheng Zhang; El-Moselhy, Tarek A.; Elfadel, Ibrahim M. and Daniel, Luca. "Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 33, no. 5 (May 2014): 728-740. © 2013 Institute of Electrical and Electronics Engineers (IEEE) https://orcid.org/0000-0002-5880-3151 en_US http://dx.doi.org/10.1109/TCAD.2013.2295818 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) Prof. Daniel via Phoebe Ayers |
| spellingShingle | El-Moselhy, Tarek A. Elfadel, Ibrahim M. Zhang, Zheng Daniel, Luca Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification |
| title | Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification |
| title_full | Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification |
| title_fullStr | Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification |
| title_full_unstemmed | Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification |
| title_short | Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification |
| title_sort | calculation of generalized polynomial chaos basis functions and gauss quadrature rules in hierarchical uncertainty quantification |
| url | http://hdl.handle.net/1721.1/108269 https://orcid.org/0000-0002-5880-3151 |
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