Do you get a whining, buzzing noises as well?
Does it matter if you are running the ICE (internal combustion engine) or running off of the battery (EV mode)?
Does the noise go away after several minutes after the car is completely off?
Sounds like the inverter cooling pump is the noise culprit. It pumps coolant from the insulated \"thermos\" tank in the fender to the engine, tends to be noisest when the engine fires up from a cold start and when you stop the engine. Inverter cooling pump runs continuously, doesn\'t matter if in EV or ICE, it will still circulate though the system.
When you shut down, the system will pump the hot coolant back into the insulated tank, for use on the next start. To make sure the engine comes up to temperature faster. Those clicks and knocking noises are with the relays and normal pumping noises to get that coolant back into the tank.
Noise is annoying, but completely normal.
2002 Corolla S, Silverstream, 1.8L 1ZZ-FE (VVT-i)
2003 Matrix XRS, Cosmic Blue, 1.8L 2ZZ-GE (VVTL-i) - RIP
2009 Matrix XRS, Blue Streak, 2.4L 2AZ-FE (VVT-i)