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NEURAL NETWORKS M. Alborzi, Ph. D. Petroleum University of Technology October, 2001

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OUTLINE Neural Networks Defined Neural Networks Defined Why Neural Networks Why Neural Networks Pattern Recognition Pattern Recognition Neural Networks Application Areas Neural Networks Application Areas A Brief History of Neural Networks A Brief History of Neural Networks Training Neural Networks Training Neural Networks Advantages of Neural Networks Advantages of Neural Networks A Simple NN Package A Simple NN Package

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Neural Networks Defined A Modeling Technique Emulating the Brain A Modeling Technique Emulating the Brain

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Why Neural Networks! The Need to Emulate the Brain The Need to Emulate the Brain Facing Complex Problems Facing Complex Problems Limitation of Mathematics Limitation of Mathematics Limitation of Serial Computers Limitation of Serial Computers The Amazing Power of the Brain to Tackle complexities The Amazing Power of the Brain to Tackle complexities The Parallel Nature and the Network Nature Structure of the Brain The Parallel Nature and the Network Nature Structure of the Brain

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Pattern Recognition Mathematical / Statistical Mathematical / Statistical Syntactical Syntactical Neural Networks Neural Networks

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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

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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),

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Figure 1: The biological neuron

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Y= fh[sum( wixi)-teta] fh(x)=1 if x>0 fh(x)=0 if x<0 Figure 2: The McCulloch and Pitts model of a neuron. X1 X2 X3 OUT

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Figure 3: A comparison between M & P model of a neuron and the biological neuron. M-P model Biological Neuron Input data x i Input signal Input branches Dendrites Weights w ji Synapses w ji x i Activation Threshold L Threshold level Output yj Output signal Output branch Axon

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XOR

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Figure 4: Final connection weights: Positive reinforcing connections: Fixed k.

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Figure 5: The input logs and the output dominant rock lithologies.

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Figure 6: schematic diagram of the initial model

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No.LogUnitDescription 1DT s/ft Sonic Velocity 2ROHBg/cm 3 Bulk Density 3NPHIPUNeutron Porosity 4PEFbarn/electronPhotoelectric Factor 5GRAPIGamma Ray Table 1: The input logs

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Table 2: The output rock lithologies. No.SymbolUnitDescription 1DOLOFractionVolume of Dolomite 2LIMEFractionVolume of Limestone 3SANDFractionVolume of Sandstone 4ANHYFractionVolume of Anhydrite 5SHALFractionVolume of Shale

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Appendix H A Sample of Log Measurements and PETROS Output for Gachsaran Well No. 6 1) Input Log Measuremwents DepthLog Measurements metresDTROHBNPHIPEFGR s/ft g/cm 3 PUbarn/electronAPI A Sample of Log Measurements and PETROS Output for Well No. 6 1) Input Log Measuremwents

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DepthVolume Fractions of the Rock Constituents metresDOLOLIMESANDANHYSHAL fraction ) PETROS Output Volume Fractions

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