B747 captain reported returning to departure airport after experiencing an engine compressor stall during climb that resulted in engine shutdown.

Narrative

During climb; passing approximately 9000'; Thrust Limit was changed from CLB2 to CLB to meet SID ZZZZ 10;000' or above at ZZZZZ (ZZZ ZZZZZ1 X SID) . As thrust increased; compressor stall on ENG #4.Memory Items from QRH Engine Limit or Surge or Stall" checklist performed.Approximately 3 or 4 compressor stalls noted before throttle retarded.Reducing Thrust Lever #4 approximately half-way to idle successfully stopped the engine stalls. Nil EGT or other exceedances noted; however EGT remained similar to other engines; with approximately half the N1 value; so this was deemed to satisfy "Abnormal condition continues"; so BLEED 4 selected off in accordance with the checklist.With BLEED 4 selected off an attempt to increase thrust was made and resulted in yet another compressor stall. Again; EGT on ENG 4 a similar value to the other three engines; with a much lower N1. The combination of these observations easily satisfied "Engine indications are abnormal"; therefore ENG 4 shutdown performed as per the checklist.Requested Priority Handling with ZZZ [Center] controller; stating SOB (Side of Body); FOB (Fuel on Board) and intention to return to ZZZ. It was stressed to the controller that we had secured the engine and our situation was not time-critical; therefore we intended to dump approximately 22T of fuel before returning to ZZZ. Advised controller that this would require approximately 15 minutes; but this was subsequently amended to less than 10 minutes.Controller promptly issued vectors and authorized Fuel Jettison - which was performed from the QRH "Fuel Jettison" checklist.Upon completion of Fuel Jettison; ZZZ [Center] controllers expeditiously arranged a radar-vectored return to ILS Rwy XXL which was executed without incident in VMC conditions.ATC advised that we could taxi clear of runway; and they coordinated fire services to conduct an external inspection of the aircraft as we temporarily parked between RWYs XXL & XXR on TWY 1. Fire team observed no external damage and agreed it was safe to proceed to parking. Taxied to gate XX and flight terminated."