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.
On the numerical approximation of the Perron-Frobenius and Koopman operator.Journal of Computational Dynamics, 3(1):51– 79
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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.