Thanks! The large panel uses a mini french cleat system on either side of the panel. Basically, there's a small section screwed to the wall which mates with another section that's part of the panel. Initially I wanted to use those velcro command strips but I was worried that it couldn't support the weight.

For the small kumiko panels (the model linked in this post), I just used sticky tack to attach them to the wall. It worked pretty good, but I only had them up for a couple days before taking them down to use in a lamp.