Feedforward neural networks in forecasting the spatial distribution of the time-dependent multidimensional functions

Abstract

The neural networks are powerful as nonlinear signal processors. This paper deals with the problem of employing the feedforward neural networks (FFNNs) to simulate the time-dependent distribution of the airborne toxin in the urbanized area. The spatial distribution of the contaminant is the multidimensional function dependent on the weather conditions (wind direction and speed), coordinates of the contamination sources, the release rate, and its duration. In this paper, we try to answer what topology should be the multilayered FFNN to forecast the contaminant strength correctly at the given point of the urbanized area at a given time. The comparison between the FFNNs is made based on the standard performance measures like correlation R and mean square error (MSE). Additionally, the new measure estimating the quality of the neural networks forecasts in subsequent time intervals after the release is proposed. In combination with R and MSE, the proposed measure allows identifying the well-trained network unambiguously. Such a neural network may enable creating an emergency system localizing the contaminant source in an urban area in real-time. However, in such a system time of answer depends directly on the multiple times run dispersion model computational time. This time is expected in minutes for custom dispersion models in urban areas and can be shortened to seconds in the case of artificial neural networks.