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Rapid experimental advances now enable simultaneous electrophysiologicalrecording of neural activity at single-cell resolution across large regions ofthe nervous system. Models of this neural network activity will necessarilyincrease in size and complexity, thus increasing the computational cost ofsimulating them and the challenge of analyzing them. Here we present a novelmethod to approximate the activity and firing statistics of a general firingrate network model (of Wilson-Cowan type) subject to noisy correlatedbackground inputs. The method requires solving a system of transcendentalequations and is fast compared to Monte Carlo simulations of coupled stochasticdifferential equations. We implement the method with several examples ofcoupled neural networks and show that the results are quantitatively accurateeven with moderate coupling strengths and an appreciable amount ofheterogeneity in many parameters. This work should be useful for investigatinghow various neural attributes qualitatively effect the spiking statistics ofcoupled neural networks. Matlab code implementing the method is freelyavailable at GitHub (\url{http://github.com/chengly70/FiringRateModReduction}).

Practical Approximation Method for Firing Rate Models of Coupled Neural Networks with Correlated Inputs