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

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

4. Neural Networks Defined • A Modeling Technique Emulating the Brain

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

7. Pattern Recognition • Mathematical / Statistical • Syntactical • Neural Networks

8. 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

9. 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),

10. Figure 1: The biological neuron

11. X1 X2 X3 OUT 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.

12. 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 Figure 3: A comparison between M & P model of a neuron and the biological neuron.

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

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

16. Figure 6: schematic diagram of the initial model

17. 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

18. 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 Table 2: The output rock lithologies.

19. Appendix H A Sample of Log Measurements and PETROS Output for Gachsaran Well No. 6 1) Input Log Measuremwents 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

20. 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