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NEURAL NETWORKSNEURAL NETWORKS
M. Alborzi, Ph. D.
Petroleum University of Technology
October, 2001
OUTLINEOUTLINE
Neural Networks DefinedNeural Networks Defined Why Neural NetworksWhy Neural Networks Pattern RecognitionPattern Recognition Neural Networks Application AreasNeural Networks Application Areas A Brief History of Neural NetworksA Brief History of Neural Networks Training Neural NetworksTraining Neural Networks Advantages of Neural NetworksAdvantages of Neural Networks A Simple NN PackageA Simple NN Package
Neural Networks DefinedNeural Networks Defined
A Modeling Technique Emulating A Modeling Technique Emulating the Brainthe Brain
Neural NetworksNeural Networks
A mathematical model that can acquire
artificial intelligence. It resembles brain in
two respects
Knowledge is acquired by network through a learning process
Inter-neuron connection strengths known as weights are used to store the knowledge
Why Neural Networks!Why Neural Networks!
The Need to Emulate the BrainThe Need to Emulate the Brain Facing Complex ProblemsFacing Complex Problems Limitation of MathematicsLimitation of Mathematics Limitation of Serial ComputersLimitation of Serial Computers The Amazing Power of the Brain to Tackle The Amazing Power of the Brain to Tackle
complexitiescomplexities The Parallel Nature and the Network The Parallel Nature and the Network
Nature Structure of the BrainNature Structure of the Brain
Pattern RecognitionPattern Recognition
Mathematical / StatisticalMathematical / Statistical SyntacticalSyntactical Neural NetworksNeural Networks
Neural Networks Applications in Pattern Classification and Pattern Recognition
• Speech recognition and speech generation • Prediction of financial indices such as currency exchange rates• Location of radar point sources• Optimization of chemical processes• Target recognition and mine detection• Identification of cancerous cells• Recognition of chromosomal abnormalities• Detection of ventricular fibrillation• Prediction of re-entry trajectories of spacecraft • Automatic recognition of handwritten characters• Sexing of faces• Recognition of coins of different denominations• Solution of optimal routing problems such as theTraveling Salesman Problem• Discrimination of chaos from noise in the prediction of time series
A Brief History of Neural Networks
• 1943 McCulloch and Pitts Model
• 1962 Rosenblatt Perceptron
• 1969 Miskey and Papert Report on the Shortcomings of Perceptron
• 1987 Rumelhart and McClleland
Breakthrough, Multilayer Perceptron (Originally from Werbos),
Figure 1: The biological neuron
Y= fh[sum( wixi)-teta]
fh(x)=1 if x>0fh(x)=0 if x<0
Figure 2: The McCulloch and Pitts model of a neuron.
X1
X2
X3
OUT
Figure 3: A comparison between M & P model of a neuron and the biological neuron.
M-P model Biological Neuron ------------------------------------------------------------ Input data xi---------------------------Input signal
Input branches------------------------Dendrites Weights wji----------------------------Synapses
wjixi-----------------------------------Activation
Threshold L---------------------------Threshold level Output yj------------------------------Output signal Output branch------------------------Axon
XOR
Figure 4: Final connection weights: Positive reinforcing connections: Fixed k.
Figure 5: The input logs and the output dominant rock lithologies.
Figure 6: schematic diagram of the initial model
No. Log Unit Description
1 DT s/ft Sonic Velocity
2 ROHB g/cm3 Bulk Density
3 NPHI PU Neutron Porosity
4 PEF barn/electron Photoelectric Factor
5 GR API Gamma Ray
Table 1: The input logs
Table 2: The output rock lithologies.
No. Symbol Unit Description
1 DOLO Fraction Volume of Dolomite
2 LIME Fraction Volume of Limestone
3 SAND Fraction Volume of Sandstone
4 ANHY Fraction Volume of Anhydrite
5 SHAL Fraction Volume of Shale
Depth Log Measurements
metres DT ROHB NPHI PEF GR
s/ft g/cm3 PU barn/electron API
2505.00 52.700 2.820 1.220 4.820 34.100
2505.15 52.800 2.800 1.470 4.670 33.600
2505.30 52.700 2.790 1.540 4.640 30.400
... ... ... ... ... ...
... ... ... ... ... ...
2667.30 49.200 2.740 3.870 4.590 23.000
2667.46 49.100 2.720 3.880 4.630 23.000
2667.61 49.100 2.720 3.880 4.680 23.000
A Sample of Log Measurements and PETROS Output for Well No. 6 1) Input Log Measuremwents
Depth Volume Fractions of the Rock Constituents
metres DOLO LIME SAND ANHY SHAL
fraction fraction fraction fraction fraction
2505.00 0.420 0.000 0.260 0.240 0.080
2505.15 0.500 0.000 0.300 0.120 0.080
2505.30 0.520 0.000 0.300 0.100 0.080
... ... ... ... ... ...
... ... ... ... ... ...
2667.30 0.420 0.580 0.000 0.000 0.000
2667.46 0.380 0.620 0.000 0.000 0.000
2667.61 0.360 0.640 0.000 0.000 0.000
2) PETROS Output Volume Fractions
NN AdvantagesNN Advantages
Model function does not have to be known
NN learns behavior by self-tuning its parameters
NN has the ability to discover patterns
NN provides a rapid and confident prediction
NN is fast-responding systems
NN can accept more input to improve accuracy,
such continuous enrichment of the NN “knowledge”
leads to more accurate predictive model
NN Problems & ChallengesNN Problems & Challenges
Design of NN:
Number of hidden layers
Number of neurons in each hidden layer
The learning constant that controls speed of
training
NN Problems & ChallengesNN Problems & Challenges
Generalization Vs. Over Fitting
New training algorithms (cross validation)
Hybrid systems (genetic algorithms)
Neural network architectureNeural network architecture
INPUTHIDDEN
API
Rs
g
T
OUTPUT
Bob
Pb
A Simple Neural Networks A Simple Neural Networks PackagePackage
Neural network architectureNeural network architecture
INPUTHIDDEN
API
Rs
g
T
OUTPUT
Bob
Pb
Thank You for Your AttentionThank You for Your Attention