W. Huang et al. / Ocean Engineering 30 (2003) 22752295
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vector W that provides the best possible approximation of the function g(X) based
on the training input [X].
The standard or basic training method is the Gradient Descent Method. In this
method, weight changes move the weights in the direction where the error declines
most quickly. Training is carried out by assigning random initial weights to each of
the neurons (usually between 0.1 and 1.0) and then presenting sets of known input
and target (output) values to the network. The network estimates the output value
from the inputs, compares the model predicted output to the target value, and then
adjusts the weights in order to reduce the mean squared difference between the net-
work output and the target values. The complete inputoutput sets are often run
through the network for several iterations (or epochs) until either the mean square
error is reduced to a given level or reaches a minimum, or until the network has
been trained for a given number of iterations.
If we let wm represent the value of weight w after mth iteration in a neuron, then
wm
wm
wm
(6)
1
where wm is the change in the weight w at the end of iteration m. It is calculated by
wm
edm
(7)
where e is the user-specified parameter controlling the proportion by which the
weights are modified. The term dm is given by
∂E
n (
dm
)
(8)
∂wm
1
n
where N is the total number of examples and E is the simulation output error.
3.3.1. Network development processes
In neural network model development, the first step is to design a specific network
architecture that includes a specific number of layers, each consisting of a certain
number of neurons. The size and structure of the network needs to match the nature
of the investigated phenomenon. Because it is usually not well known at the early
stage, the task is not easy and often involves a trial and errors approach. The new
network is then subjected to the training process. In that phase, neurons apply an
iterative process to the number of inputs (variables) to adjust the weights of the
network in order to optimally predict (in traditional terms one could say, find a fit
to) the sample data on which the training is performed. After learning from an exist-
ing data set, another new data set is used to validate or verify the performance of
the trained neural network. If the neural network performance is satisfactory in model
verification, it is capable in model predictions using other new data inputs.
3.4. Advantages of the ANN approach
One of the major advantages of neural networks is that, theoretically, they are
capable of approximating any continuous function (Haykin, 1999). The resulting
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