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Instituto Tecnológico y de Estudios Superiores de Occidente
2008-06
Fast parametric models for EM design using
neural networks and space mapping
Rayas-Sánchez, José E.; Zhang, Qi J.
Enlace directo al documento: http://hdl.handle.net/11117/600
Este documento obtenido del Repositorio Institucional del Instituto Tecnológico y de Estudios Superiores de
Occidente se pone a disposición general bajo los términos y condiciones de la siguiente licencia:
http://quijote.biblio.iteso.mx/licencias/CC-BY-NC-ND-2.5-MX.pdf
(El documento empieza en la siguiente página)
Repositorio Institucional del ITESO rei.iteso.mx
Departamento de Electrónica, Sistemas e Informática DESI - Artículos y ponencias con arbitraje
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2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
Fast Parametric Models for EM Design Using Neural Networks and Space Mapping
José E. Rayas-SánchezResearch Group on Computer-Aided Engineering of Circuits and Systems (CAECAS)
Department of Electronics, Systems and InformaticsInstituto Tecnológico y de Estudios Superiores de Occidente (ITESO)
Guadalajara, Mexico, 45090
http://www.desi.iteso.mx/caecas/
Q.J. ZhangDepartment of Electronics, Carleton University
Ottawa, Canada K1S 5B6
http://www.doe.carleton.ca/~qjz
Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC) 2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008
2
Outline
§ Brief introduction to ANNs
§ EM-based statistical analysis
§ Input Space Mapping
§ Linear-Input Neural-Output Space Mapping (LINO-SM)
§ LINO-SM approach to yield estimation
§ Constrained Broyden-Based Space Mapping
§ Training the Output Neuromapping
§ Example
§ Conclusions
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2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
3
Biological Neuron
(Kartalopoulos, 1996)
soma
axon
dendritic tree
axonic endingnucleus
4
Artificial Neural Networks (ANNs)
§ An Artificial Neural Network (ANN) is a massively parallel distributed processor made up of simple processing units, that is able of acquiring knowledge from its environment though a learning process
§ ANNs are also information processing systems that emulate biological neural networks: they are inspired in the ability of human brain to learn from observation and generalize by abstraction
![Page 4: Rayas-Sánchez, José E.; Zhang, Qi J. · 2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008 Tutorial on Advances in CAD Techniques for EM Modeling and](https://reader034.vdocument.in/reader034/viewer/2022052008/601d4ec79463e56b661df722/html5/thumbnails/4.jpg)
2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
5
Artificial Neurons
§ An artificial neuron is a simple processing unit that receives and combines signals from many other neurons
§ Common types of artificial neurons are:Linear NeuronsInner-Product Nonlinear NeuronEuclidean Distance Neuron
6
Linear Neuron
vk = [vk1 … vkn]T vector of inputs
wk = [wk1 … wkn]T vector of weighting factors
bk bias or offset term
zk activation potential or induced local field, output signal
Σ
wk1
wk2
wkn
bkvk1
vk2
vkn
zkk
Tkkk bz wv+=
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2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
7
Inner Product Nonlinear Neuron
kT
kkk bs wv+=
)( kkk sz ϕ=Σ
wk1
wk2
wkn
bkvk1
vk2
vkn
sk zk)( kk sϕ
vk = [vk1 … vkn]T inputs wk = [wk1 … wkn]T weighting factors
bk bias or offset term sk activation potential
zk output signal
ϕk(sk) activation function or squashing function
8
Typical Activation Functions
Sigmoid or logistic function
kskkk esz −+
==1
1)(ϕ
ksakkk esz −+
==1
1)(ϕ
a = 1 (), a = 0.5 (× ) and a = 2 ()
With a slope parameter
-4 -2 0 2 40
0 . 2
0 . 4
0 . 6
0 . 8
1
-2 -1 0 1 2-1
-0 .5
0
0 . 5
1
Hyperbolic tangent function
kk
kk
ss
ss
kkkk eeeessz −
−
+−=== )(tanh)(ϕ
![Page 6: Rayas-Sánchez, José E.; Zhang, Qi J. · 2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008 Tutorial on Advances in CAD Techniques for EM Modeling and](https://reader034.vdocument.in/reader034/viewer/2022052008/601d4ec79463e56b661df722/html5/thumbnails/6.jpg)
2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
9
Some ANN Paradigms
§ Multilayer Perceptrons
§ Radial Basis Functions
§ Recurrent Neural Networks
10
3-Layer Perceptrons (3LP)
TThh
Thh ][ 1 wwW L=
vWbs hh +=
Thh
hhh bbb ][ 21 L=b
where
)(sFWby oo +=
TTom
Too ][ 1 wwW L=
Tom
ooo bbb ][ 21 L=b
Thss ])()([)( 1 ϕϕ L=sF
zh
zh
z2
z2
z1
z1
y1
I1
I2 L1
Lmym
inputlayer
hiddenlayer
outputlayer
Ih
vn
v1
hh ℜ∈Fbs ,,mo ℜ∈by, hmo ×ℜ∈W hnh ×ℜ∈W
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2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
11
Automated Model Generation (AMG)
Fastneuralmodel
EM simulators(examples used:
Ansoft HFSS, Sonnet em,
Faustus MEFiSTo)
AMG
• Data sampling and generation
• ANN structure adaptation
• Over-learning detection
• Under-learning detection
• Other actions as needed
User-requiredaccuracy
12
AMG for Spiral Inductor
Data Generators: Sonnet em Ansoft-HFSS
εr
S W
….
RS11 IS11 RS12 IS12
w s ε f
0.85%Advanced AMG(KAMG-PKI)
2.34%AMG
6.25%Conventional training
Testing Error
ANN Training TechniqueAMG uses data sampling algorithm to
sample data at critical locations. With the same amount of training data, AMG obtains better model accuracy than conventional training techniques.
Model accuracy under limited training data
![Page 8: Rayas-Sánchez, José E.; Zhang, Qi J. · 2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008 Tutorial on Advances in CAD Techniques for EM Modeling and](https://reader034.vdocument.in/reader034/viewer/2022052008/601d4ec79463e56b661df722/html5/thumbnails/8.jpg)
2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
13
Inverse Modeling by Neural Network
(Waveguide Filter Example, H. Kabir, Y. Wang, M. Yu and Q. Zhang, 2006)
Data Generator: Ansoft-HFSS (3D EM)
I/O coupling iris
Coupling screws
Tuning screws
Internal coupling iris
I/O coupling iris
Input neurons: electrical parametersOutput neurons: geometrical parameters
14
Filter Dimensions By Neural Net vs Measurement
-0.0011.8641.865Cavity length
0.0040.1150.111M12/M34 coupling screws
0.0020.1350.133M22/M33 tuning screws
-0.0400.0050.045M11/M44 tuning screws
0.0040.2160.212M14 iris
-0.0020.2970.299M23 iris
00.4050.405I/O irises
Difference(inch)
Measurement(inch)
Neural Model(inch)
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2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
15
Time-Domain Modeling by Neural Networks
Location of conducting posts (d ) controls
pass band behavior
Data Generator: MEFiSTo 3D Professional
WR-28 Rectangular Waveguide Ka-band (26.5 to 40Ghz)
u(t)
τ
….
f(t)
y(t-τ ) y(t-2τ) x(t-τ ) x(t-2τ)
τ τ τ
d
Recurrent neural network (RNN)
(With see thru top)1
2a = 280 mil
a
b
b = 140 mil
d
d
16
EM and RNN Transient Responses
t (ns)
f1
0 0.2 0.4 10.6 0.8
d = 3.88 mm
d = 5.17 mm
d = 4.53 mm
f21
0 0.2 0.4 10.6 0.8
d = 3.88 mm
d = 5.17 mm
d = 4.53 mm
10
-10
0
1
-1
0
… EM test data (MEFiSTo)RNN
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2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
17
EM-based Interpolating Surrogates
for Yield Estimation using
Neural Space Mapping Methods
18
EM-based Statistical Analysis
§ Statistical analysis and yield prediction are crucial for manufacturability
§ Reliable yield prediction typically requires massive amount of high-fidelity simulations (full-wave EM simulations)
§ Performing Monte Carlo yield analysis by directly using EM simulations is not feasible for most practical problems
§ Using an interpolating surrogate based on linear-input neural-output space mapping can be a solution
![Page 11: Rayas-Sánchez, José E.; Zhang, Qi J. · 2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008 Tutorial on Advances in CAD Techniques for EM Modeling and](https://reader034.vdocument.in/reader034/viewer/2022052008/601d4ec79463e56b661df722/html5/thumbnails/11.jpg)
2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
19
Input Space Mapping
coarsemodel
xcP
finemodel
Rf (xf ,ψ)ψ
xf
Rc(P(xf),ψ)
finemodel
Rf (xf ,ψ)ψxf coarse
modelxc
ψRc(xc,ψ)
Rf (xfSM,ψ) ≈ Rc(xc
*,ψ)
L Rc(P(xfSM)) can not
accurately estimate the fine model yield around xf
SM
☺
20
Linear-Input Neural Output Space Mapping
coarsemodel
xcP
finemodel
Rf (x f ,ψ)ψ
xf
w
QANN
Rc(P(x f),ψ)
Q(Rc(P(xf),ψ), xf,ψ, w)
),(),,),,(( * ??? ffffc xRwxcBxRQ =+for all xf and ψ in the training region
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2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
21
LINO-SM approach to Yield Estimation
Calculate xf SM and P through
input space mapping
Generate learning and testing data around xf
SM according to tolerances
Start
End
Obtain xc* by optimizing
the coarse model
Obtain Q by training an output neuro mapping
Calculate yield using Q(Rc(P(xf),ψ),xf,ψ))
22
Constrained Broyden-Based SM
(2) 2
21minarg)( T
pT
cf ee
xxP …=
),(),()( jccsjffsfj ?? xRxRxe −=
(1) )),((minarg* ?U cc
cc xR
xx =
xfSM = x f
(i ) cBxxP += ff )(
where B = B(i ) and c = xc* − Bxf
SM
Begin find xc
* solving (1) i = 0, xf
(i) = xc*, B(i) = I, δ = 0.3
*)()( )( cif
i xxPf −= using (2)
repeat until stopping_criterion solve )()()( iii fhB −= for h(i)
)()()( iif
testf hxx +=
while max)(min)(f
testff
testf xxxx f≺ ∨
)()( ii hh δ= )()()( ii
ftestf hxx +=
end )()1( test
fif xx =+
*)1()1( )( cif
i xxPf −= ++ using (2)
)()(
)()1()()1(
iTi
Tiiii
hh
hfBB+
+ += , i = i + 1
end
![Page 13: Rayas-Sánchez, José E.; Zhang, Qi J. · 2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008 Tutorial on Advances in CAD Techniques for EM Modeling and](https://reader034.vdocument.in/reader034/viewer/2022052008/601d4ec79463e56b661df722/html5/thumbnails/13.jpg)
2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
23
Generating Learning and Testing Points
testing base pointlearning base point
xfSM
xf 1
xf 2
xf 3
2n+1 learning base points in a star distribution2n testing base points in a rotated star distribution
24
Training the Output Neuro Mapping
Begin Generate RCL, RCT, RFL and RFT
FFLCLoldL |||| RR −=ε , FFTCT
oldT |||| RR −=ε
h = m, i = 1
FLi ||)(||minarg)( wE
ww =
FFLi
LL ||)(|| )( RwQ −=ε
FFTi
TT ||)(|| )( RwQ −=ε
while TLToldT εεεε ≥∨≥
ToldT εε = , L
oldL εε = , i = i + 1, h = h + 1
FLi ||)(||minarg)( wE
ww =
FFLi
LL ||)(|| )( RwQ −=ε
FFTi
TT ||)(|| )( RwQ −=ε end
)1(* −= iww end
),(),,),,(( * ??? ffffc xRwxcBxRQ =+ for all xf and ψ in the training region
)()( wQRwE LFLL −=
![Page 14: Rayas-Sánchez, José E.; Zhang, Qi J. · 2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008 Tutorial on Advances in CAD Techniques for EM Modeling and](https://reader034.vdocument.in/reader034/viewer/2022052008/601d4ec79463e56b661df722/html5/thumbnails/14.jpg)
2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
25
Microstrip Notch Filter
εr
H
W50
W50
Lc
Lp
W50
W50
Lc
Lc
W50
W50
Lp
SgSg
Lo
Lo
Lo
xf = [Lc Lo Sg]T
H = 10milW50 = 31milεr = 2.2loss tan = 0.0009(RT Duroid 5880)
Specifications:|S21| ≤ 0.05 for 13.19GHz ≤ f ≤ 13.21GHz
|S21| ≥ 0.95 for f ≤ 13GHz and f ≥ 13.4GHz
26
Microstrip Notch Filter – Fine Model
1
2
Hair
ygap
ygap
ygap
Hair = 60 milLp = ½(Lo+Lc)Ygap = Logrid = 0.5mil×0.5mil
![Page 15: Rayas-Sánchez, José E.; Zhang, Qi J. · 2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008 Tutorial on Advances in CAD Techniques for EM Modeling and](https://reader034.vdocument.in/reader034/viewer/2022052008/601d4ec79463e56b661df722/html5/thumbnails/15.jpg)
2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
27
Microstrip Notch Filter – Coarse Model
MclinMclin
W=W50L=LcS=Sg
Mclin
W=W50L=W50
W=W50L=LcS=Sg
outin
W=W50L=LcS=Sg
W=W50L=W50
var W50 31milvar Lp 31mil var Lzero 1e-9mil
W=W50L=Lp
W=W50L=Lp
MSub RT-Duroid-5880H=10milER=2.2TAND=0.0009LEVEL=2
var Lc 143milvar Lo 158milvar Sg 8mil
Preassigned Parameters:Optimization Variables:
L=LoW=W50 L=Lzero
W=W50
L=LoW=W50
L=LzeroW=W50
L=LoW=W50 L=Lzero
W=W50
28
Microstrip Notch Filter – Starting Point
12.7 12.8 12.9 13 13.1 13.2 13.3 13.4 13.5 13.6 13.70
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
frequency (GHz)
S21
Rc(xc*)
Rf (xc*)xc
* = [143 158 8]T (mil)
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2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
29
Microstrip Notch Filter – SM Solution
12.7 12.8 12.9 13 13.1 13.2 13.3 13.4 13.5 13.6 13.70
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
frequency (GHz)
S21
Rc(P(xfSM))
Rf (xfSM)xf
SM = [143.5 159 8]T (mil)
30
Microstrip Notch Filter – Training Q
0 1 2 3 4 5-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
hidden neurons, h
log10
(εL)
log10(εT)
tolerance region: ±0.5mil
![Page 17: Rayas-Sánchez, José E.; Zhang, Qi J. · 2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008 Tutorial on Advances in CAD Techniques for EM Modeling and](https://reader034.vdocument.in/reader034/viewer/2022052008/601d4ec79463e56b661df722/html5/thumbnails/17.jpg)
2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
31
Microstrip Notch Filter – LINOSM Solution
12.7 12.8 12.9 13 13.1 13.2 13.3 13.4 13.5 13.6 13.70
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
frequency (GHz)
S21
Rc(P(x fSM
))
Rf (xfSM
)
Q(Rc(P(x fSM
)), x fSM
)
32
Microstrip Notch Filter – LISM Yield
12.7 12.8 12.9 13 13.1 13.2 13.3 13.4 13.5 13.6 13.70
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
frequency (GHz)
S21
Rc(P(x
f))
for xf around xfSM
Yield = 98 %
max dev: ±0.2mil
![Page 18: Rayas-Sánchez, José E.; Zhang, Qi J. · 2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008 Tutorial on Advances in CAD Techniques for EM Modeling and](https://reader034.vdocument.in/reader034/viewer/2022052008/601d4ec79463e56b661df722/html5/thumbnails/18.jpg)
2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)
Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico
33
Microstrip Notch Filter – LINOSM Yield
12.7 12.8 12.9 13 13.1 13.2 13.3 13.4 13.5 13.6 13.70
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
frequency (GHz)
S21
Q(Rc(P(x
f)), x
f)
for x f around xfSM
Yield = 58 %
max dev: ±0.2mil
34
Conclusions
§ We described a method for highly accurate EM-based statistical analysis and yield estimation of RF and microwave circuits
§ It consists of applying a constrained Broyden-based linear-input space mapping, followed by a neural-output space mapping, in which the responses, the design parameters and independent variable are mapped
§ The output neuromodel is trained using reduced sets of learning and testing samples
§ The resultant interpolating surrogate model is used as a very efficient vehicle for accurate statistical analysis and yield prediction