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1.5
1
0.5
0
−0.5
−1
−1.5
10
5
10
5
0
0
−5
y
−5
x
−10
−10
Fig. 12.17
Approximation of the test function of Eq. (
12.26
), using an RBF neural network with
Gaussian basis functions
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
10
5
10
5
0
0
−5
y
−5
x
−10
−10
Fig. 12.18
Test function of Eq. (
12.27
)
Table
12.1
demonstrates the final RMSE values, succeeded by neural networks
with Hermite basis functions (Hermite-FNN), the one hidden layer FNN with
sigmoidal basis functions (OHL-FNN) and the RBF with Gaussian activation
functions, after 50 epochs.
From Table
12.1
, it is observed that in function approximation problems, neural
networks with Hermite basis functions perform at least as well as one hidden layer
FNN with sigmoidal activation functions (OHL-FNN) and RBF with Gaussian
activation functions. As expected, the number of nodes of the hidden layer of the
OHL-FNN and the variance of the Gaussian basis functions of the RBF affect the
quality of function approximation. In the case of 1D functions Hermite-based neural
