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By Shahab D. Mohaghegh (Ed.), Saud M. Al-Fattah (Ed.), Andrei S. Popa (Ed.)

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A-I4) Eq. A-I4 gives the weight change in a link between Layer j and an output layer. 1/ usually is called the learning rate and takes any value between 0 and 1. The higher the learning rate, the higher the weight changes. 2) during early stages oflearning and that it be increased as the net begins to converge. , links between Layers i and j). AWij is defined as AWij = -1/(8EI8wij)' ............................ (A-IS) The output, OPj' from a node in the middle (hidden) Layer j because of Pattern P is defined as The derivation that follows is similar to that for the case when the link is connected to the output layer.

F;;y' ............................. (D-I) (Fig. D-I). The model has two similar patterns, one smaller in size with longer beginning and ending positions as compared with the other. Using the scaling method AI-Kaabi and Lee proposed, we obtain scaled versions of the two patterns (Fig. D-2). We see that after scaling, the shapes have been altered considerably. Thus, if Pattern 1 was used as a training set for Model A, the neural net probably would not identify Pattern 2 as Model A.

Peterson chair In Petroleum Engineering at Texas A&M U. A. Holdltch and Assocs. _ _ __ _- - ' cal adviser at Lee AI-Kaabl Exxon Co. A. and a senior research specialist at Exxon Production Research Co. Lee holds BChE, MS, and PhD degrees In chemical engineering from Georgia Tech. He Is a member of the Career Guidance and Archie Scholarship committees and the Emerging/Peripheral Technical Committee. Lee Is a Distinguished Service Award winner and a member of the National Academy of EngineerIng. Azlz U.

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