The paper combines McCann interpolation and JKO Wasserstein gradient flow with differentiable persistent homology to iteratively retarget persistence diagrams and update filtrations, but it provides only qualitative 2D examples and no proof that the data follows the claimed Wasserstein dynamics.
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Dynamical Persistent Homology via Wasserstein Gradient Flow
The paper combines McCann interpolation and JKO Wasserstein gradient flow with differentiable persistent homology to iteratively retarget persistence diagrams and update filtrations, but it provides only qualitative 2D examples and no proof that the data follows the claimed Wasserstein dynamics.