Certain aspects of the present disclosure provide methods and apparatus for a continuous-time neural network event-based simulation that includes a multi-dimensional multi-schedule architecture with ordered and unordered schedules and accelerators to provide for faster event sorting; and a formulation of modeling event operations as anticipating (the future) and advancing (update/jump ahead/catch up) rules or methods to provide a continuous-time neural network model. In this manner, the advantages include faster simulation of spiking neural networks (order(s) of magnitude); and a method for describing and modeling continuous time neurons, synapses, and general neural network behaviors.