As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
PILOT REPORTED THAT DURING INITIAL CLIMB TO FL190 THE N1, N2 & FUEL FLOW ON THE NR 1 ENG BEGAN TO SURGE UP & DOWN & THEN STABILIZED. THE PILOT ELECTED TO RETURN TO THE DEPARTURE AIRPORT & MADE A NORMAL APPROACH & LANDING. THE ENG RETURNED TO NORMAL OPERATION DURING THE DESCENT. AFTER EXTENSIVE TROUBLESHOOTING DETERMINED THE N2 TRANSDUCER WAS FAULTY. THE SENSOR WAS REPLACED & THE ENG RAN NORMALLY. A TEST FLIGHT WAS MADE TO VERIFY THE CORRECTIVE ACTION.