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.

翻译：神经网络是一类非常通用的模型，能够学习多个变量之间的各种关系。在实际应用中，特别值得关注的关系之一是非线性系统的输入-输出关系，这类关系具有广泛的应用前景。研究能够估计此类关系的模型是一个涉及众多理论与实际成果的广阔学科。神经网络虽然非常通用，但存在多种特例，包括专为图像处理和序列处理等特定应用调整的卷积神经网络和循环神经网络。我们提出一个假设：通过将频率信息纳入网络结构来调整通用网络，应能使网络特别适合非线性系统辨识。此外，我们从理论角度证明，可以在不丧失通用性的前提下添加这种频率信息。我们将这种新结构称为频率支持神经网络（FSNN），并对其性质进行了实证研究。