Maximum-Entropy Density Estimation for MRI Stochastic Surrogate Models

Zhang, Zheng; Farnoosh, Niloofar; Klemas, Thomas J.; Daniel, Luca

doi:10.1109/lawp.2014.2349933

Cited by 5 publications

(7 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Given μ j , σ 2 j , and higher moments of R j [35], f (R j ) in ( 28) can be approximated using the existing PDF estimation techniques, e.g., the moment matching technique [37] and the maximum entropy technique [38]. Then, the integrals in u j (x 0 ) can be evaluated by applying the Gauss quadratures developed in [39].…”

Section: A Formulation Of the Objective Function For Yield-driven Em Optimization Incorporating Pc Coefficientsmentioning

confidence: 99%

“…. ., T −1 (x 0 , ξ (M) )} using (38). Then, an existing EM simulator is driven to evaluate the EM responses R j (T −1 (x 0 , ξ (l) )) and the EM sensitivities…”

Section: Pc-based Yield Optimization Algorithmmentioning

confidence: 99%

“…. , ξ (M) } into a set of EM geometrical parameter samples around the nominal point using (38). Step 5: Numerically evaluate the PC coefficients a i j (x 0 ) using ( 6)-( 8) and the derivatives of each PC coefficient with respect to the nominal point using (39).…”

Section: Pc-based Yield Optimization Algorithmmentioning

confidence: 99%

See 2 more Smart Citations

Polynomial Chaos-Based Approach to Yield-Driven EM Optimization

Zhang

Feng

et al. 2018

IEEE Trans. Microwave Theory Techn.

View full text Add to dashboard Cite

Yield-driven optimization is important in microwave design due to the uncertainties introduced in the manufacturing process. For the first time, we extend in this paper the use of polynomial chaos (PC) approach from electromagnetic (EM)-based yield estimation to EM-based yield optimization of microwave structures. We first formulate a novel objective function for yield-driven EM optimization. By incorporating the PC coefficients into the formulation, the objective function is analytically related to yield optimization variables, which are the nominal point. We then derive the sensitivity formulas of the PC coefficients with respect to the nominal point, following which we derive the sensitivities of the optimization objective function with respect to yield optimization variables. These sensitivities are then used in gradient-based optimization algorithms to find the optimal yield solution iteratively. The proposed objective function requires fewer EM simulations to provide reliable yield representation than that in the conventional Monte Carlo-based yield optimization approach. As a result, the number of EM simulations required to find the update direction and suitable step size for the change of the nominal point is reduced at each iteration of optimization. This allows the proposed approach to achieve similar yield increase using much fewer EM simulations or greater yield increase using similar number of EM simulations compared to the conventional yield optimization approach. The advantages of our proposed approach are demonstrated by yield-driven EM optimization of three waveguide filter examples.

show abstract

Section: A Formulation Of the Objective Function For Yield-driven Em Optimization Incorporating Pc Coefficientsmentioning

confidence: 99%

“…. ., T −1 (x 0 , ξ (M) )} using (38). Then, an existing EM simulator is driven to evaluate the EM responses R j (T −1 (x 0 , ξ (l) )) and the EM sensitivities…”

Section: Pc-based Yield Optimization Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

Polynomial Chaos-Based Approach to Yield-Driven EM Optimization

Zhang

Feng

et al. 2018

IEEE Trans. Microwave Theory Techn.

View full text Add to dashboard Cite

show abstract

“…Once the generalized polynomial-chaos expansion (1) is obtained, various statistical information of the performance metric y(ξ) can be obtained. For instance, the expectation and standard deviation of y(ξ) can be obtained analytically; the density function of y(ξ) can be obtained by sampling (1) or by using the maximum-entropy algorithm [40].…”

Section: Generating Stochastic Model (1)mentioning

confidence: 99%

A big-data approach to handle process variations: Uncertainty quantification by tensor recovery

Zhang

Weng

Daniel

2016

2016 IEEE 20th Workshop on Signal and Power Integrity (SPI)

Self Cite

View full text Add to dashboard Cite

Fabrication process variations are a major source of yield degradation in the nano-scale design of integrated circuits (IC), microelectromechanical systems (MEMS) and photonic circuits. Stochastic spectral methods are a promising technique to quantify the uncertainties caused by process variations. Despite their superior efficiency over Monte Carlo for many design cases, these algorithms suffer from the curse of dimensionality; i.e., their computational cost grows very fast as the number of random parameters increases. In order to solve this challenging problem, this paper presents a high-dimensional uncertainty quantification algorithm from a big-data perspective. Specifically, we show that the huge number of (e.g., 1.5 × 10 27 ) simulation samples in standard stochastic collocation can be reduced to a very small one (e.g., 500) by exploiting some hidden structures of a high-dimensional data array. This idea is formulated as a tensor recovery problem with sparse and low-rank constraints; and it is solved with an alternating minimization approach. Numerical results show that our approach can simulate efficiently some ICs, as well as MEMS and photonic problems with over 50 independent random parameters, whereas the traditional algorithm can only handle several random parameters.

show abstract

“…It is noted that (5.26) and (5.27) have different intervals for the integration, i.e., For notational convenience, we defineū j (x 0 ) as a yield indicator w.r.t. the specification sample S j as follows Given µ j , σ 2 j , and higher moments of R j [93], f (R j ) in (5.28) can be approximated using existing PDF estimation techniques, e.g., the moment matching technique [113] and the maximum entropy technique [114]. Then the integrals inū j (x 0 ) can be evaluated by applying the Gauss quadratures developed in [115].…”

Section: Formulation Of the Objective Function For Yield-driven Em Opmentioning

confidence: 99%

Advanced Parametric Modeling and Yield Optimization Approaches for Microwave Passive Components

Zhang¹

View full text Add to dashboard Cite

Parametric modeling and yield optimization techniques play important roles in electromagnetic (EM)-based microwave component design. In the first part of this thesis, we propose a novel training approach for parametric modeling of microwave passive components with respect to changes in geometrical parameters using matrix Padé via Lanczos (MPVL) and EM sensitivities. In the proposed approach, the EM responses of passive components versus frequency are represented by polezero-gain transfer functions. The relationships between the poles/zeros/gain in the transfer function and geometrical variables are learnt by neural networks. A novel

show abstract

Maximum-Entropy Density Estimation for MRI Stochastic Surrogate Models

Cited by 5 publications

References 21 publications

Polynomial Chaos-Based Approach to Yield-Driven EM Optimization

Polynomial Chaos-Based Approach to Yield-Driven EM Optimization

A big-data approach to handle process variations: Uncertainty quantification by tensor recovery

Advanced Parametric Modeling and Yield Optimization Approaches for Microwave Passive Components

Contact Info

Product

Resources

About