B787 pilot reported the engine N1 value was less than expected after engine start. Maintenance was not able to fix the problem and the aircraft was taken out of service.

Narrative

I was Relief Pilot on the flight. After pushback and engine start; the FO received the load closeout and accomplished the procedures to check Takeoff Data. She immediately noticed the EICAS Ref N1 was approximately 2% below the performance data value. She made several attempts to get a more reasonable Ref N1 but was unsuccessful. The ramp tower needed us to move for incoming traffic so we contacted ground and were given instructions to taxi to an uncongested area. The FO tried several different uplinks different data requests; TO2 (Take Off thrust setting); TO1 etc. She also tried deleting the assumed temperature on each data upload. None of these attempts improved the 2% deficit in Ref N1. During this time; the captain was in contact with maintenance and we tried everything maintenance suggested but nothing improved the low Ref N1. We returned to the gate and maintenance crew chiefs and avionics specialists attempted to correct the issue; to include a full power down and reboot of the aircraft; but were unable to change anything. The aircraft was eventually taken out of service. I was concerned about this anomaly and wanted more information about our procedures and the technical details of how the FMC calculates Ref N1; where it gets the inputs for Temp and Pressure Altitude; and if there are any other factors that input into the Ref N1 calculation. With regard to the procedures; I cannot find any definitive information about how to check Ref N1 against the performance data predicted value. What I've been taught is that the number has to be 'reasonable'. It's my understanding that Ref N1 is only using Temp and PA (Pressure Altitude) so I would always expect Ref N1 to be at or above performance data value; but the reason we say 'reasonable' is because there might be a temporary hot temp due to asphalt; jet engine exhaust; etc. I emailed the 787 contacts and called the training department to get procedural/technical advice. I have not yet heard back from either one. After about a week; I looked at the electronic logbook for the aircraft and saw that the aircraft was returned to service with what I believe to be an engine run. A few days later; there was a write-up that indicated the TO1 was derated to 10% instead of 5% and the TO2 was derated to 20% instead of 15%. This explains why we had the 2% N1 deficit. This event made me aware our procedures on how to specifically check N1 are vague. I've talked to several other pilots and there is not a standard interpretation on how to check Ref N1 with N1 and what the definition of 'reasonable' is. I don't have the technical background to give a specific answer to the causal factor; but it's my understanding the TO1 and TO2 de-rate percentages are programmed in to the FMC without any pilot input. If that's the case; then it's a programming issue. I don't have any mitigation suggestions for how to improve the programming accuracy of the FMC.To mitigate the potential of a crew departing with an N1 below the performance data predicted value (which could cause takeoff distance available to be less than balanced field length); I would recommend we develop a more specific procedure to check T/O Data after Load Closeout.