We use Neural Network approach to derive a Runge{Kutta{Nystr om pair of orders 8(6) for the integration of orbital problems. We use an di erential evolution optimization technique to choose the free parameters of the method's family. We train the method to perform optimally in a speci c test orbit from the Kepler problem for a speci c tolerance. Our measure of e ciency involves the global error and the number of function evaluations. Other orbital problems are solved to test the new pair.