scholarly journals Iterative Optimization Algorithms to Determine Transmit and Receive Weights for MIMO Systems

10.5772/15413 ◽  
2011 ◽  
Author(s):  
Osamu Muta ◽  
Takayuki Tominaga ◽  
Daiki Fujii ◽  
Yoshihiko Akaiw
Keyword(s):  
Mimo Systems ◽  
Optimization Algorithms ◽  
Iterative Optimization

Evaluation of Pettys Nonlinear Model in Wood Permeability Measurement

Holzforschung ◽  
2001 ◽  
Vol 55 (1) ◽  
pp. 82-86
Author(s):  
J. Lu ◽  
F. Bao ◽  
Y. Zhao
Keyword(s):  
Nonlinear Model ◽  
Gas Permeability ◽  
Optimization Algorithms ◽  
Optimization Techniques ◽  
Curvilinear Relationship ◽  
Grid Search ◽  
Permeability Measurement ◽  
Iterative Optimization ◽  
Starting Values ◽  
Least Squares Fit

Summary To calculate the effective radii of two conductive elements in series in wood specimens by using the gas permeability measurement, the four parameters from the curvilinear relationship of superficial specific permeability against reciprocal mean pressure as illustrated in Petty's model must be evaluated. This paper describes a detailed procedure for obtaining such parameters by using the least-squares fit calculated from a statistical analysis system (SAS) program. Three different iterative optimization algorithms and starting points were used separately to fit the Petty's nonlinear model based on the same experimental data from one specimen of birch. The estimate of the parameters: A = 35.38 darcy, B = 80.51 darcy, l = 0.19 darcy atm, m = 6.34 darcy atm was recommended for the fitted model. Compared to the results on the estimate of parameters obtained in the previous papers, this estimate for the parameters was a global minimum, thus it was a refinement and more accurate. Since the Gauss-Newton method resulted in almost the same convergence results for all the three sets of starting values with the least iterations in the evaluation, it was the preferred optimization algorithm both for simplicity and accuracy in solving the Petty's model. Because the same solutions for all three iterative optimization algorithms were obtained by using two different sets of starting points produced from the grid search, a grid search seemed to be very helpful for finding reasonable starting values for various iterative optimization techniques.

scholarly journals Inverse Design for Silicon Photonics: From Iterative Optimization Algorithms to Deep Neural Networks

2021 ◽  
Vol 11 (9) ◽  
pp. 3822
Author(s):  
Simei Mao ◽  
Lirong Cheng ◽  
Caiyue Zhao ◽  
Faisal Nadeem Khan ◽  
Qian Li ◽  
...  
Keyword(s):  
Neural Networks ◽  
Silicon Photonics ◽  
Design Methodology ◽  
Degrees Of Freedom ◽  
Deep Neural Networks ◽  
Low Cost ◽  
Optimization Algorithms ◽  
Optimization Methods ◽  
Inverse Design ◽  
Iterative Optimization

Silicon photonics is a low-cost and versatile platform for various applications. For design of silicon photonic devices, the light-material interaction within its complex subwavelength geometry is difficult to investigate analytically and therefore numerical simulations are majorly adopted. To make the design process more time-efficient and to improve the device performance to its physical limits, various methods have been proposed over the past few years to manipulate the geometries of silicon platform for specific applications. In this review paper, we summarize the design methodologies for silicon photonics including iterative optimization algorithms and deep neural networks. In case of iterative optimization methods, we discuss them in different scenarios in the sequence of increased degrees of freedom: empirical structure, QR-code like structure and irregular structure. We also review inverse design approaches assisted by deep neural networks, which generate multiple devices with similar structure much faster than iterative optimization methods and are thus suitable in situations where piles of optical components are needed. Finally, the applications of inverse design methodology in optical neural networks are also discussed. This review intends to provide the readers with the suggestion for the most suitable design methodology for a specific scenario.

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