Solving the inverse problem in groundwater flow by iterative inversion of a neural network

Abstract

A new methodology for solving the inverse problem in groundwater hydrology is developed and applied to a synthetic case study. An innovative aspect of the methodology is the use of a data driven approximation of the groundwater flow equation to calibrate a numerical model for a steady state groundwater system. An Artificial Neural Network (ANN) was successfully trained to produce the resulting hydraulic map when a complete transmissivity field is prescribed. The trained network was then iteratively inverted to match the prior information on transmissivity as well as piezometric head measurements. The hydraulic head maps resulting from the transmissivity field produced by the inverted ANN. are in good agreement with the hydraulic head maps produced from the original synthetic transmissivity field. The study shows that there is no unique solution to the inverse problem, and that an ensemble of solutions that honor the transmissivity measurements at their locations, and closely match the measured hydraulic head values can be obtained. Further more, the study shows that each of these non-unique solutions can be used to obtain accurate predictions.