We propose a method, based on Neural Networks, that detects the nonlinear robust interplanetary solar wind variables, with varying delays, driving the coupled behavior of three geomagnetic indices (Dst, AL, and AU). As opposed to minimizing a prediction error, the method is based on degrading the prediction by distorting the inputs of the trained Neural Networks in order to highlight the most sensible drivers. We show that the $z$ component of the magnetic field, the duskward oriented electric field, and the speed of the particles of the interplanetary medium, at particular time delays, seem to be the most efficient drivers of the three coupled geomagnetic indices. Using only the sensible or robust drivers in the model, we demonstrate that iterated predictions during geomagnetic storm are significantly improved from models that only use one of the outstanding drivers with multiple time delays. The derived robust nonlinear Neural Network model is also a significant improvement over linear approximations, specially when used as iterated predictors.