For a quadcopter, flying close underneath a flat surface will increase the amount of lift produced, but this will make it harder to control (unless the quadcopter is equipped with appropriate control software).
According to comments by Alex and Peter Kämpf, if you fly a quadcopter close underneath a flat surface, the quadcopter will tend to get "sucked up" and collide with the surface. You will have to reduce power dramatically in order to go back down.
You could probably make a quadcopter under a ceiling easier to control by equipping it with a proximity sensor (or perhaps an accelerometer) and software which automatically reduces power when the aircraft gets close to a ceiling. It could take a lot of tuning, but with the right control algorithm, it would probably be easy to maintain a constant distance under the ceiling.
So, why does a quadcopter behave this way? I don't know if any research has been done on this, but I can make an educated guess.
For aircraft flying above a flat surface, the ground effect increases the amount of lift produced. When the wings are near the ground, a high-pressure region is created between the wings and the ground, thereby increasing the amount of lift.
So for aircraft flying below a flat surface, presumably something similar happens. The propellers create a low-pressure region between themselves and the upper surface. That once again increases the amount of lift produced.
(In the extreme case, with an object which is in contact with the upper surface, it's possible for the object to create a low-pressure region above itself, and thereby keep itself up, using no power at all. That's what a suction cup is.)
For posterity, here are the comments by Alex and Peter Kämpf that I referenced above:
I can say that when I fly my smaller sized quads indoors that its more of a suction cup response. The few that I have all have generally the same effect. If I fly to close to the ceiling I end up sucked up to it where then I have to dramatically drop throttle before they are released. It takes a surprisingly little amount of power to maintain the suction effect. Keep in mind they all have duct motors with a flat surface on top (no camera or antenna sticking in the way) so that may provide more suction action as well. – Alex 2019-01-16 15:50:56Z
There is an important difference: While 'regular' ground effect is dynamically stable, this inverted ground effect is the opposite. Coming close to the ceiling means that the quadcopter will be sucked up until it collides with the ceiling. – Peter Kämpf 2019-01-16 16:26:17Z