probably magnetically, by making a rectangle of nonadhesive magnetic strips and gluing the filter to the strips with something like silicone caulk-- essentially a DIY demci filter. or i may just glue the filter straight onto the side panel with caulk if thickness is an issue or if the strip doesn't hold securely enough. the nice thing about using silicone is that it peels off cleanly if you ever have to remove it. this stuff is vacuum/compressed air cleanable, though, so that shouldn't ever be necessary.
*edit: i should add that the filter material would be on the inside of the side panel, so none of this would be visible. on the bottom, it would just be sandwiched in place underneath the fans.
another option, if you're adding adhesive acoustic damping material to the inside of the panels, is to just use that to hold down the filter mesh.