Optimal Design : Surrogate Models
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Optimal Design : Surrogate Models Kuei-Yuan Chan National Taiwan University 1
Transcript of Optimal Design : Surrogate Models
Optimal Design : Surrogate Models
Kuei-Yuan ChanNational Taiwan University
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A good model should represent reality in the simplest meaningful manner.
A surrogate model is a simpler analysis model extracted from the more sophisticated ones using a variety of data-handling techniques.
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Model forms
• Analytical models in mathematical form : based on fundamental science with proper assumptions. Generally easier to calculate but with limited applications.
• Computer simulations : most commonly used in engineering practice. These codes are wrapped within a graphical user interface (GUI). One must understand the limitations and assumptions behind these computer logics.
• Experiment data fitting : also one of the most common practice in engineering. Although in math forms, it does not provide basic science and usually limited to interpolations.
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Wind Tunnel with Fluid Dynamics Modeling
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credit to 陳亮宇、沈育儒、柯曼德、楊敦仁、徐征宇
Curve fitting with various models
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0
5
10
15
20
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Linear and Quadratic Fits and Least Squares
• Let be the approximation function.
• The least square best linear fit is the function such that
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Expensive
x1
x2
...xm
y1
y2
...ym
y
mina0,a1
�m⇤
i=1
yi � yi
⇥2
subject to yi = aT1 xi + a0
Neural Network Modeling
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Basic Neuron
• Basic neuron without bias
• Basic neuron with bias
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General Neural Network Model
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y(x) = �
�n⇤
i=1
wixi + b
⇥weights
activation function
Kriging Modeling
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Kriging Model
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y(x) = f(x) + z(x)
f(x) = � = (IT R�1I)�1IT R�1yR(xi,xj) = e
�
n�
k=1
�k|xik � xj
k|2
� = argmin�|R| 1
m ⇥2⇥
⇥2 =1m
(y � �I)R�1(y � �I)
is in the form
where
with
Matlab Functions
• NEWFF
• TRAIN
• kriging demo.zip
• kriging-ych.zip
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