Geostatistics has become a preferred tool for the identification of lithofacies from sparse data, such as measurements of hydraulic conductivity and porosity. Recently we demonstrated that the support vector machine (SVM), a tool from machine learning, can be readily adapted for this task, and offers significant advantages. On the conceptual side, the SVM avoids the use of untestable assumptions, such as ergodicity, while on the practical side, the SVM out performs geostatistics at low sampling densities. In this study, we use the SVM within an inverse modeling framework to incorporate hydraulic head measurements into lithofacies delineation, and identify the directions of feuture research.