An efficient tool for accelerating the numerical solution of the stochastic subsurface flow problem using neural networks

Abstract

An efficient numerical solution for the two-dimensional groundwater flow problem using artificial neural networks (ANNs) is presented. Under stationary velocity conditions with unidirectional mean flow, the conductivity realizations and the head gradients, obtained by a traditional finite difference solution to the flow equation, are given as input-output pairs to train a neural network. The ANN is trained successfully and a certain level of recognition of the relationship between input conductivity patterns and output head gradients is achieved. The trained network produced velocity realizations that are physically plausible without solving the flow equation for each of the conductivity realizations. This is achieved in a small fraction of the time necessary for solving the flow equations. The prediction accuracy of the ANN reaches 97.5% for the longitudinal head gradient and 94.7% for the transverse gradient. Head-gradient and velocity statistics in terms of the first two moments are obtained with a very high accuracy. The cross covariances between head gradients and the fluctuating log-conductivity (log-K) and between velocity and log-K obtained with the ANN approach match very closely those obtained by a traditional numerical solution. The same is true for the velocity components auto-covariances. The results are also extended to transport simulations with very good accuracy. Spatial moments (up to the fourth) of mean-concentration plumes obtained using ANNs are in very good agreement with the traditional Monte Carlo simulations. Furthermore, the concentration second moment (concentration variance) is very close between the two approaches. Considering the fact that higher moments of concentration need more computational effort in numerical simulations, the advantage of the presented approach in saving long computational times is evident. Another advantage of the ANNs approach is the ability to generalize a trained network to conductivity distributions different from those used in training. However, the accuracy of the approach in cases with higher conductivity variances is being investigated.