Support vector machines (SVMs) for monitoring network design

Abstract

In this paper we present a hydrologic application of a new statistical learning methodology called support vector machines (SVMs). SVMs are based on minimization of a bound on the generalized error (risk) model, rather than just the mean square error over a training set. Due to Mercer's conditions on the kernels, the corresponding optimization problems are convex and hence have no local minima. In this paper, SVMs are illustratively used to reproduce the behavior of Monte Carlo–based flow and transport models that are in turn used in the design of a ground water contamination detection monitoring system. The traditional approach, which is based on solving transient transport equations for each new configuration of a conductivity field, is too time consuming in practical applications. Thus, there is a need to capture the behavior of the transport phenomenon in random media in a relatively simple manner. The objective of the exercise is to maximize the probability of detecting contaminants that exceed some regulatory standard before they reach a compliance boundary, while minimizing cost (i.e., number of monitoring wells). Application of the method at a generic site showed a rather promising performance, which leads us to believe that SVMs could be successfully employed in other areas of hydrology. The SVM was trained using 510 monitoring configuration samples generated from 200 Monte Carlo flow and transport realizations. The best configurations of well networks selected by the SVM were identical with the ones obtained from the physical model, but the reliabilities provided by the respective networks differ slightly.