Memory effects description by neural networks with delayed feedback connections

For the purpose of dynamical systems modelling it was proposed to include feedback connections or delay elements in the classical feedforward neural network structure so that the present output of the neural network depends on its previous values. These delay elements can be connected to the hidden and/or output neurons of the main neural network. Each delay element gets a value of a state variable at a past. time instant and keeps this value during a single sampling period. The groups of delay elements record the values of the state variables for a given time period in the past. Changing the number of the delay elements, which belongs to one group, a shorter or a longer time period in the past can be accounted for. Thus, the connection weights determine the influence of the past process states on the present state in a similar way as it is in the time delay kernel or CER-MF models. Specific feedforward neural networks with time delay connections are employed to solve the problem of neural network chemostat modelling as well as specific kinetic rates modelling. The obtained during models training weights of the feedback connections are discussed as the points of a time delay kernel or as the strength levels in a CER model (the points in the CER-MF). The corresponding changes in these weights with changing of the time period in the past that is accounted for are shown.