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According to [ 21], a standard definition of the training error E of a hypothesis is given by (4) E (w → ) ≡ 1 2 ∑ d ∈ D (t d − o d ) 2, where D is the set of training examples, t d is the target output for training example d, and o d is the output of the network for d.

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Through out the work, PAM STAMP 2G® finite element (FE) code is used to simulate the tensile behavior and to generate output data required for training the ANN.

In this way, some input output data consisting of uncertain parameters of system and controller parameters as inputs and probability of failure of some cost functions as output are used for training such GMDH-type neural networks which replace the very time consuming direct solution of dynamical systems during the MCS.

The data set elements (i.e., inputs and outputs) for training NNs were calculated from analytic equations based on restrictions.

From the mean of ten random seeds, a maximum excitatory feed-forward synaptic strength of 3 nS was found to be optimal for training the output layer across all five transforms.

After training each layer, its output is considered as the input for training the next layer.

The agreement between the experimental observations and the network output (predictions) for training is shown in Figure 2.

Hence, the selection of input and output data for training the network is very important for the successful implementation of the network.

Out of the total input/output data sets, 80% was used for training the model and 20% for checking to validate the model.

It is to note that these results are in fact carried out by configuring the proposed fuzzy-based neural network approach through the training of the RBFNN via the PSO algorithm, where the differences between real and target output for all training data can be apparent.

Additional elements presented by the companies included: version stamp for model output, training datasets with tutorials available to users, validation datasets that remain with the software to allow verification of continued system model reliability, and transparency regarding source of data and assumptions within the system.

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