We show that known Newton-type laws for Optimal Mass Transport, Schroedinger Bridges and the classic Madelung fluid can be derived from variational principles on Wasserstein space. The second order differential equations are accordingly obtained by annihilating the first variation of a suitable action.
Extremal curves in wasserstein space
Pavon, Michele
2017
Abstract
We show that known Newton-type laws for Optimal Mass Transport, Schroedinger Bridges and the classic Madelung fluid can be derived from variational principles on Wasserstein space. The second order differential equations are accordingly obtained by annihilating the first variation of a suitable action.
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