A granular recurrent neural network for multiple time series prediction

We present a computing scheme as a variant of a recently proposed granular recurrent neural network. Being deduced from a generic system of partial differential equations, this variant is able to capture the spatiotemporal variability of some datasets and problems. The convergence of the computing scheme has been formally discussed. Some preliminary numerical experiments were first performed by using synthetic datasets, inferring some particular partial differential equations. Then two application examples were considered (by using publicly available datasets), namely the prediction of dissolved oxygen in surface water simultaneously at different depths (unlike the current literature) and the prediction of the concentration of particulate matter less than 2.5 μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu$$\end{document}m in diameter at different sites. The numerical results show the potential of the approach for forecast against well-known techniques such as Long Short-Term Memory networks.