Direct kinematics (DK) is one of the most challenging problem for cable-driven parallel robot (CDPR) with sagging cables. Solving the DK in real-time is not an issue provided that a guess of the solution is available. But difficulties arise when all DK solutions have to be determined (e.g. in the design phase of the CDPR). Continuation and interval analysis have been proposed to find the solutions but they are computer intensive. A preliminary investigation on the use of classical neural networks (NN) for the DK has shown that they were performing poorly. We present in this paper several methodological improvements that allows to get on average 99.95% of the exact DK solutions in about 5 seconds. Still this result is not completely satisfactory and we present possible axis to obtain better results in terms of exact results and multiple solutions.