Valid approximation of spatially distributed grain size distributions - A priori information encoded to a feedforward network

This paper presents a model for the approximation of multiple, spatially distributed grain size distributions based on a feedforward neural network. Since a classical feedforward network does not guarantee to produce valid cumulative distribution functions, a priori information is incor porated into the model by applying weight and architecture constraints. The model is derived in two steps. First, a model is presented that is able to produce a valid distribution function for a single sediment sample. Although initially developed for sediment samples, the model is not limited in its application; it can also be used to approximate any other multimodal continuous distribution function. In the second part, the network is extended in order to capture the spatial variation of the sediment samples that have been obtained from 48 locations in the investigation area. Results show that the model provides an adequate approximation of grain size distributions, satisfying the requirements of a cumulative distribution function.