I was assuming the material is rigid (which is wrong). So my idea (continuing the suggestion of parent) was to put / remove air from the surrounding volume to t

I was assuming the material is rigid (which is wrong). So my idea (continuing the suggestion of parent) was to put / remove air from the surrounding volume to the mylar balloon (which means, in the aerogel) to modify the density of the system and thus the buoyancy. This would require energy to run the pump, so it is not clear this would be more efficient than normal air balloons (but would be less dangerous, since no fire is needed). Of course, nothing mentioned here makes any sense since the material is not rigid.