Parametric system identification, which is the process of uncovering the inherent dynamics of a system based on the model built with the observed inputs and outputs data, has been intensively studied in the past few decades. Recent years have seen a surge in the use of neural networks (NNs) in system identification, owing to their high approximation capability, less reliance on prior knowledge, and the growth of computational power. However, there is a lack of review on neural network modelling in the paradigm of parametric system identification, particularly in the time domain. This article discussed the connection in principle between conventional parametric models and three types of NNs including Feedforward Neural Networks, Recurrent Neural Networks and Encoder-Decoder. Then it reviewed the advantages and limitations of related research in addressing two major challenges of parametric system identification, including the model interpretability and modelling with nonstationary realisations. Finally, new challenges and future trends in neural network-based parametric system identification are presented in this article
