This is an idea I've thought about on and off for a while but never tried out. Essentially my thinking was that rather than formulating an animation as a description how the positions of vertices change, what if the vertex positions are constant and the animation how the shape of space changes.
Thinking of it like how a magnet distorts field lines is the most visual representation I can think of.
It obviously isn't a generally useful approach, much more suited to organic animation, but I'd be interested what people think. Or maybe this is already used and has some names I can look up online.