Diffeomorphisms and vector fields are uniquely identifiable from finitely many pushforward densities or weighted divergences, with the number of required observations determined by embedding theorems.
The Takens embedding theorem.International Journal of Bifurcation and Chaos, 1(04):867–872, 1991
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On the Unique Recovery of Transport Maps and Vector Fields from Finite Measure-Valued Data
Diffeomorphisms and vector fields are uniquely identifiable from finitely many pushforward densities or weighted divergences, with the number of required observations determined by embedding theorems.