Interpolation of 2D water content distribution and uncertainty assessment using a neural network that does not require prior training

Abstract

This study investigated the applicability of spatial interpolation using a convolutional neural network that requires no pre-training (DIP) to the non-uniform, two-dimensional water content distribution of peat ground. In experiments that progressively reduced the number of training boreholes, a simple shallow model, which reproduces local variations well, gave the lower error under dense conditions, whereas a complex deep model, which preserves broad-scale trends, gave the lower error under sparse conditions; the two exchanged places between 29 and 19 training boreholes. This position was consistent with all of the three splits obtained by changing the choice of test boreholes. The uncertainty (standard deviation) derived from multiple trials corresponded not to the horizontal distance from the nearest borehole but to the vertical spacing of the data and to changes in soil properties, in contrast to Gaussian process regression (GPR), whose uncertainty depends on geometric distance. This standard deviation does not express the probability of containing the true value, but it can be used as an index for selecting candidate locations for additional investigation.