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Original Articles

Estimation of initial condition in heat conduction by neural network

, &
Pages 317-328 | Received 11 Jan 2002, Accepted 15 Feb 2003, Published online: 13 Oct 2011

Figures & data

FIGURE 1 Two activation functions: (a) sigmoid ; (b) .

FIGURE 1 Two activation functions: (a) sigmoid ; (b) .

FIGURE 2 The backpropagation neural network with one hidden layer.

FIGURE 2 The backpropagation neural network with one hidden layer.

FIGURE 3 Gaussian for three differents variances.

FIGURE 3 Gaussian for three differents variances.

FIGURE 4 Cascade correlation network with two hidden layers. The symbols denotes a neuron.

FIGURE 4 Cascade correlation network with two hidden layers. The symbols denotes a neuron.

FIGURE 5 Sample of test-functions for training: (a) non-similar functions; (b) similar functions.

FIGURE 5 Sample of test-functions for training: (a) non-similar functions; (b) similar functions.

TABLE I Training results for the neural networks used for initial condition reconstruction

TABLE II Activation results for the noiseless experimental data

FIGURE 6 Reconstruction using multilayer perceptron NN with noiseless data.

FIGURE 6 Reconstruction using multilayer perceptron NN with noiseless data.

FIGURE 7 Reconstruction using radial basis function NN with noiseless data.

FIGURE 7 Reconstruction using radial basis function NN with noiseless data.

FIGURE 8 Reconstruction using cascade correlation NN with noiseless data.

FIGURE 8 Reconstruction using cascade correlation NN with noiseless data.

FIGURE 9 Reconstruction using multilayer perceptron NN with 5% of noise.

FIGURE 9 Reconstruction using multilayer perceptron NN with 5% of noise.

FIGURE 10 Reconstruction using radial basis function NN with 5% of noise.

FIGURE 10 Reconstruction using radial basis function NN with 5% of noise.

FIGURE 11 Reconstruction using cascade correlation NN with 5% of noise.

FIGURE 11 Reconstruction using cascade correlation NN with 5% of noise.

TABLE III Activation results for the experimental data with 5% of noise

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