A worked example of feed-forward neural network calculations.
In the particular case of a 3-5-1 neural network that was trained on a small data set to model Chesapeake Bay phytoplankton production, the W and Z matrices were:
I0 (surface irradiance), B (phytoplankton biomass) and Zp (photic zone depth) were used as network inputs and were scaled in the [0,1] interval, assuming a fixed arbitrary maximum value for each input variable. These values were:
where the first element corresponds to I0, the second to B and the third to Zp. For example, the input values:
are scaled and passed to the input nodes ij as:
Hence, the input vector is:
where the last element is constant and corresponds to the bias node.
The network output (i.e. the predicted PP) is computed by carrying out the forward propagation as shown in the general description of EBP NN. Since in the training patterns also the output variable (PP) was scaled into a [0,1] interval, the network output has to be scaled back to the original units:
With PPmax=3 and PPoffset=0.15, the predicted PP value is 2.479 g C m-2 day-1. Other predicted values can be easily computed following the same procedure with different xraw input vectors.
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