Spherical Harmonic Optimal Transport: Application to Climate Models Comparisons

ArXi:2605.18389v1 Announce Type: new Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their, but comes with an expensive computational cost, hindering its potential application to real world use cases. On manifolds, convolutional algorithms based on the heat kernel have been proposed to alleviate this cost, but their theoretical properties remain largely unexplored. We establish that the heat kernel cost converges to the optimal transport cost as time vanishes in the balanced and unbalanced cases.