A neural network solution for a complicated experimental High Energy Physics problem is described. The method is used to reconstruct the momentum and charge of muons produced in collision of particles in the ATLAS detector. The information used for the reconstruction is limited to the output of the outer layer of the detector, after the muons went through strong and inhomogeneous magnetic field that have bent their trajectory. It is demonstrated that neural network solution is efficient in performing this task. It is shown that this mechanism can be efficient in rapid classification as required in triggering systems of the future particle accelerators. The parallel processing nature of the network makes it relevant for hardware realization in the ATLAS triggering system. ©2001 American Institute of Physics.