# Neural Networks Architecture for Modeling of Complex Static Systems

## Single-Input Single-Output Feedforward Neural Network (SISO-FFNN)

To model complex static systems, three NN-based architectures can be adopted. The most basic structure proposed is a SISO-FFNN utilizing complex input/output signals [6], as illustrated in Figure 7.4. In this architecture, a complex input is modified with a set of complex valued weights before entering the input layer. The output of each neuron goes to the next layer of neurons and modified again with another set of complex weights and biases before it gets added in the final layer to obtain final output. Each neuron *neuron ^{l}i* consists of complex input, complex weights, bias, and activation function. This architecture introduces complex valued weights and activation functions, which usually result in cumbersome calculations and divergence when training the network. The input-output relationship of this model can be expressed as:

where the output of the of any neuron at an intermediate layer can be calculated using the same scheme described by Equations 7.1 and 7.2. The main difference here is that the synaptic weights (гр, the biases *(b ^{l}),* as well as the activation functions (f), are complex valued.

Figure 7.4 Single-input single-output feedforward neural network