Regularized Artificial Neural Network Training for Biased Data of Soil Hydraulic Parameters

Development and application of artificial neural network (ANN) pedotransfer functions for estimating soil hydraulic properties (SHP) have become popular in the last two decades. However, limited availability of SHP training data often constrains the full potential of improved SHP estimation with ANN in many practical situations. In many situations, SHP data are limited and could be biased by samples from a restricted portion of the data population. Artificial neural network pedotransfer functions developed under such situations are likely to yield biased estimates. We proposed a direct approach to minimize mean estimation errors (bias) in such situations and developed a regularized ANN algorithm. The new algorithm revised the ANN error function and its gradients with respect to neural network outputs. We applied the new algorithm to synthetically generated SHP data representing different data availability situations and found that the newly developed algorithms were effective in reducing bias. Training with both the new and conventional mean square error functions resulted in equally good results in test phases when ANN models were trained with randomly sampled unbiased data. However, when ANN was trained with and applied to SHP data with respectively different means (biased sample), the proposed regularized ANNwas highly effective in minimizing the bias when compared with ANN with the conventional mean square error function.