A method of maintaining a desired downhole pressure during a drilling operation can include measuring a parameter with a sensor, communicating actual parameter values from the sensor to a predictive device, training the predictive device to output predicted parameter values in response to input of the actual parameter values, and outputting the predicted parameter values from the predictive device when the predictive device ceases receiving the actual parameter values. A well drilling system can include a predictive device which outputs predicted parameter values in response to input of actual parameter values to the predictive device. The predictive device continues to output the predicted parameter values, even when the predictive device fails to receive valid actual parameter values. Another well drilling system includes a data validator which communicates valid actual parameter values to the predictive device, but does not communicate invalid actual parameter values to the predictive device.