Frequency-Supported Neural Networks for Nonlinear Dynamical System Identification

Neural networks are a very general type of model capable of learning various relationships between multiple variables. One example of such relationships, particularly interesting in practice, is the input-output relation of nonlinear systems, which has a multitude of applications. Studying models capable of estimating such relation is a broad discipline with numerous theoretical and practical results. Neural networks are very general, but multiple special cases exist, including convolutional neural networks and recurrent neural networks, which are adjusted for specific applications, which are image and sequence processing respectively. We formulate a hypothesis that adjusting general network structure by incorporating frequency information into it should result in a network specifically well suited to nonlinear system identification. Moreover, we show that it is possible to add this frequency information without the loss of generality from a theoretical perspective. We call this new structure Frequency-Supported Neural Network (FSNN) and empirically investigate its properties.