A method for operating a fan system as well as such a fan system. The fan system has a control device having an artificial neural network. The control device controls an electric motor of a backward curved centrifugal fan. The centrifugal fan creates a gas flow that is characterized by an actual flow value, particularly the actual value of a volume flow rate. The actual flow value is not detected by a sensor means, but determined by means of the artificial neural network depending from input variables and based thereon, the electric motor is open loop or closed loop controlled by means of the control device. The motor current and the motor voltage as well as their time-dependent behavior that can be the time derivative (e.g. gradient of first order) or that can be at least one preceding value at a preceding point in time, are provided to an input layer of the artificial neural network. It is particularly advantageous, if the artificial neural network determines an actual value of an output pressure that is fed back internally or externally forming an input variable for the input layer.