Bayesian Artificial Intelligence Model Averaging for Hydraulic Conductivity Estimation

Abstract

This research presents a Bayesian artificial intelligence model averaging (BAIMA) method that incorporates multiple artificial intelligence (AI) models to estimate hydraulic conductivity and evaluate estimation uncertainties. Uncertainty in AI model outputs stems from errors in model input and nonuniqueness in selecting different AI methods. Using one single AI model tends to bias the estimation and underestimate uncertainty. The BAIMA employs a Bayesian model averaging (BMA) technique to address the issue of using one single AI model for estimation. The BAIMA estimates hydraulic conductivity by averaging the outputs of AI models according to their model weights. In this study, the model weights are determined using the Bayesian information criterion (BIC) that follows the parsimony principle. The BAIMA calculates the within-model variances to account for uncertainty propagation from input data to AI model output. Between-model variances are evaluated to account for uncertainty because of model nonuniqueness. The authors employ Takagi-Sugeno fuzzy logic (TS-FL), an artificial neural network (ANN), and neuro-fuzzy (NF) to estimate hydraulic conductivity for the Tasuj plain aquifer, Iran. The BAIMA combines three AI models and produces better fitting than individual models. Although NF was expected to be the best AI model owing to its utilization of both the TS-FL and ANN models, the NF model is nearly discarded by the parsimony principle. The TS-FL model and the ANN model show equal importance, although their hydraulic conductivity estimates are quite different. This results in significant between-model variances that are normally ignored by using one AI model.