[geezerjay]

> but a case where multiple different outcomes can arise from identical inputs.

If they are identical but not equal and these small differences in the input lead to large deviations in the output then that's pretty much the definition of a chaotic system.

Edit: I've just browsed through the paper in question and it actually demonstrates thar an approximate (weak) solution is not unique, which means that the exact same inputs in may have multiple weak form solutions.

[fspeech]

"Weak" here does not mean numerical approximations. These are mathematicians so any quantitative approximation would be bounded o(1) otherwise the work would be meaningless. One should think of "weak" as in constraints, for example constraints at lower spatial resolutions (but precise).