Most flows of engineering interest are turbulent. Direct numerical or scale-resolved simulations (DNS) of turbulent flows could provide all of the information desired about such flows. However, these simulations are highly demanding computationally and are not feasible with today's computing capabilities. Currently, turbulent flows of engineering interest are typically addressed by performing simulations based on the Reynolds Averaged Navier-Stokes (RANS) equations with the eddy-viscosity model. Despite the tremendous progress made, more research is still needed in developing more accurate and more broadly applicable eddy-viscosity models. Steve Pope in a JFM paper published in 1975 the most general expression for the eddy-viscosity model, and that model involves a finite number of tensors and invariants constructed from the mean strain and rotation rates. All eddy-viscosity models that utilize the Boussinesq approximation use only one of those tensors. In this study, supervised machine learning based on neural networks is used to explore the full extent of Pope's general expression for the eddy-viscosity model. The test problems used in this exploratory study are the one-dimensional fully-developed incompressible Couette and channel flows. These problems were selected because excellent models exist for these turbulent flows, and so can serve as a check on the usefulness of supervised learning based on neural networks in creating better models. The neural network is trained by using DNS data to identify the best coefficients for the general expression of the eddy viscosity given by Pope.