In response to the comments in this thread that seem to argue that our understanding of gravity as just as good as our understanding of rubber deformation or in some way good enough, I would agree with the parent that our non-understanding of gravity is quite starkly different from our understanding of the deformation of rubber.

We really do understand the deformation of rubber in terms of local molecular interactions. Not in analogies but in actual detail of what the molecules are doing. The partial differential equations that give us the computational short-cut to solve the shape of the rubber can nevertheless be derived from first principles, and computed using local mechanisms that model exactly what the universe does.

In the case of gravity, we know the shape of the field, but we have no idea what local interactions are yielding them.