Wavelet neural networks: A complete framework and current state of research

The wavelet neural networks (WNNs) have emerged as one of the most powerful computational models for solving complex nonlinear problems across various domains. They are thus currently a focus for many researchers. WNNs combine neural networks (NNs) from artificial intelligence with the robust mathematical framework of wavelets. This review paper aims to explore and present the current status of research in the field of WNN. To start with, a brief description of NNs is provided along with the history, construction and types of wavelets. Based on the literature review, we have categorized WNNs into three categories, namely, wavelet activation NNs (WANN), wavelet synapse NNs (WSNN) and wavelet transformation NNs (WTNN). These three types of WNNs are discussed in detail, including their construction and applications. The pros and cons of each type of WNN are also presented. Another focus of this paper is to identify the types of wavelets that have majorly been used till now and also the wavelets which are less common in WNN structures. Despite significant progress, several research gaps remain, it has been found that only a few of the first-generation wavelets, namely the Morlet, Gaussian and Mexican-hat wavelets, have been used in WNNs hitherto. Along with the literature and gaps, this research paper demonstrates that the incorporation of wavelets into a NN algorithm improves the accuracy and enhances the capability of capturing physical features in the model. It can be used as a guide to further the work in the field of WNNs.