Exact adjoint sensitivity analysis for neural-based microwave modeling and design.pdf
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1、226IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 51, NO. 1, JANUARY 2003 Exact Adjoint Sensitivity Analysis for Neural-Based Microwave Modeling and Design Jianjun Xu, Student Member, IEEE, Mustapha C. E. Yagoub, Member, IEEE, Runtao Ding, and Qi Jun Zhang, Senior Member, IEEE AbstractFo
2、r the first time, an adjoint neural network method is introduced for sensitivity analysis in neural-based microwave modeling and design. The proposed method is appli- cable to generic microwave neural models including variety of knowledge-based neural model embedding microwave empirical information.
3、 Through the proposed technique, efficient first- and second-order sensitivity analysis can be carried out within the microwave neural network infrastructure using neuron responses in both the original and adjoint neural models. A new formulation of simultaneous training of original and adjoint neur
4、al models allows robust model development by learning not only the input/output behavior of the modeling problem, but also its derivative data. The proposed technique is very useful for neural-based microwave optimization and synthesis, and for ana- lytically unified dc/small-signal/large-signal dev
5、ice modeling and circuit design. Examples of high-speed very large scale integration system interconnect modeling and optimization, large-signal FET modeling, and three-stage power-amplifier simulation utilizing the proposed sensitivity technique are demonstrated. Index TermsDesign automation, model
6、ing, neural networks, sensitivity. I. INTRODUCTION A RTIFICIAL neural networks have been recently recog- nized as a useful vehicle for RF and microwave modeling and design 1. Neural network models can be trained from electromagnetic (EM)/physics simulation or measurement data and subsequently used d
7、uring circuit analysis and design. The models are fast and can represent EM/physics behaviors it learned, which otherwise are computationally expensive. Var- ious types of inputoutput information in linear and nonlinear microwave design have been used for neural network learning, such as EM solution
8、s versus geometrical/physical parameters 24, signal integrity solutions versus electrical parameters 5, transistor electrical parameter versus electrical parameters 6, transistor electrical versus physical parameters 7, and more. The learning ability of neural networks is very useful when an analyti
9、cal model for a new device is not available, e.g., modeling of a new transistor. A neural network can also generalize, meaning that the model can respond to new data that has not been used during training. Neural models can be more accurate than polynomial regression models, handle more Manuscript r
10、eceived September 19, 2001. J. Xu and Q. J. Zhang are with the Department of Electronics, Carleton University, Ottawa, ON, Canada K1S 5B6. M. C. E. Yagoub is with the School of Information Technology and Engineering, University of Ottawa, Ottawa, ON, Canada K1N 6N5. R. Ding is with the School of Ele
11、ctronics and Information Engineering, Tianjin University, Tianjin 300072, China. Digital Object Identifier 10.1109/TMTT.2002.806910 dimensions than lookup table models, and allow more automa- tion in model development than conventional circuit models. Microwave researchers have demonstrated this app
12、roach in a variety of applications such as modeling and optimization of high-speed very large scale integration (VLSI) interconnects 2, coplanar waveguide (CPW) circuits 8, spiral inductors 9, microwave FETs and amplifiers 10, 11, CMOS and HBTs 12, 13, global modeling 14, and yield optimization and
13、circuit synthesis 10, 15, 16. Knowledge-based ap- proaches combining microwave empirical or equivalent-circuit models together with neural network learning have also been studied 7, 17, 18 to further improve the training efficiency and model reliability. Thispaper addressesa newtaskinthisarea,i.e.,n
14、eural-based sensitivityanalysis.Sensitivityinformationisveryim- portant for circuit optimization 19, 20, and for unified dc/small-signal/large-signal modeling and circuit design 21. In the case of neural networks, first-order sensitivity analysis has been studied, e.g., for networks with binary resp
15、onses for signal-processing purposes 22 and for multilayer perceptron structures used in microwave modeling and design 16, 23. However, to perform sensitivity analysis in more generic neural model structures including embedded microwave knowledge, and to train the networks to learn from sensitivity
16、data that arise during microwave modeling, remain an unsolved task. For the first time, a novel adjoint neural network sensitivity analysistechnique is presented in thispaper, which allows exact sensitivity to be calculated in a general neural model accommo- datingmicrowaveempiricalfunctions,equival
17、entcircuit,aswell as conventional switch-type neurons in an arbitrary neural net- workstructure.Theadjointneuralnetworkstructureisexcitedby aunitexcitationcorrespondingtotheoutputneuronsintheorig- inalneuralnetwork.Anewformulationallowsthetrainingofthe adjoint neural models to learn from derivative
18、training data. An elegantderivationis presentedwherethefirst-andsecond-order derivative calculation are carried out using the neural network infrastructure through a combination of back-propagation pro- cesses in both the original and adjoint neural networks. Using thesecond-orderderivative,weareabl
19、etotrainaneuralnetwork model to learn not only microwave input/output data, but also its derivative information, which is very useful in simultaneous dc/small-signal/large-signal device modeling. InSectionII,themicrowaveneuralmodelingproblemissum- marized. In Section III, we formulate the new adjoin
20、t sensi- tivity technique and present its structure including descriptions of adjoint neurons and links, and element derivative neurons (EDNs). We then formulate a combined training of original and 0018-9480/03$17.00 2003 IEEE XU et al.: EXACT ADJOINT SENSITIVITY ANALYSIS FOR NEURAL-BASED MICROWAVE
21、MODELING AND DESIGN227 adjoint neural networks and derive the sensitivity formulas for bothfirst-andsecond-orderderivativesusingtheneuralnetwork error propagation infrastructure. In Section IV, the proposed sensitivity analysis technique is applied to high-speed VLSI in- terconnect modeling and opti
22、mization, large-signal FET mod- eling, and three-stage power-amplifier simulation examples. II. MICROWAVENEURALMODELING: PROBLEMSTATEMENT Letrepresent an-vector containing parameters of a mi- crowave device/circuit, e.g., gate length and gatewidth of an FET, or width and spacing of transmission line
23、s. Letrepre- sent a-vector containing the responses of the device/circuit under consideration, e.g., drain current of an FET, or mutual inductance between transmission lines. The physics/EM rela- tionship betweenandcan be highly nonlinear and multidi- mensional. The theoretical model for this relati
24、onship may not be available (e.g., a new semiconductor device), theory may be too complicated to implement, or the theoretical model may be computationally too intensive for online microwave design and repetitive optimization (e.g., three-dimensional full-wave EM analysis inside a Monte Carlo statis
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