# Spherical Harmonic Optimal Transport: Application to Climate Models Comparisons

arXiv: https://arxiv.org/abs/2605.18389 · HTML: https://mlsanity.com/paper/2605.18389/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 58 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 5 of 5)

- [Sinkhorn Divergences for Unbalanced Optimal Transport](https://mlsanity.com/paper/1910.12958/) (2019)
- [DISCO: accurate Discrete Scale Convolutions](https://mlsanity.com/paper/2106.02733/) (2021)
- [FlashSinkhorn: IO-Aware Entropic Optimal Transport on GPU](https://mlsanity.com/paper/2602.03067/) (2026)
- [Entropic regularisation of unbalanced optimal transportation problems](https://mlsanity.com/paper/2305.02410/) (2023)
- [Convergence rates for regularized unbalanced optimal transport: the discrete case](https://mlsanity.com/paper/2507.07917/) (2025)

## Abstract (arXiv)

Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, 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. In the specific case of the 2-sphere mathbbS2, we ensure that the associated Sinkhorn divergences retains the desirable geometric and analytic properties of classical optimal transport discrepancies. Moreover, we leverage the harmonic structure of the sphere to derive a fast Sinkhorn algorithm, requiring only O(n) memory and O(n3/2) time per iteration, with fully dense GPU-friendly operations. We validate its computational efficiency on synthetic data, and discuss its potential use in the evaluation of global climate models, providing both spatial and seasonal insights into models performances.