Can an ascending aortic aneurysm shrink by itself?

Unlikely: This is very unlikely. Aneurysms treated endovascularly (stents / endografts) do often shrink because they are depressurized.

Not Likely: Aneurysms are dilated blood vessels. They are not going to shrink. Sometimes they are wrapped with material to keep them from stretching further, but usually that section of the vessel needs replaced or reinforced with a stent.