Spherical Harmonic Optimal Transport: Application to Climate Models Comparisons
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913143357177856 |
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| author | Houédry, Pierre Legheraba, Iskander Buecher, Léo Courty, Nicolas |
| author_facet | Houédry, Pierre Legheraba, Iskander Buecher, Léo Courty, Nicolas |
| contents | 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 $\mathbb{S}^2$, 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 $\mathcal{O}(n)$ memory and $\mathcal{O}(n^{3/2})$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_18389 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spherical Harmonic Optimal Transport: Application to Climate Models Comparisons Houédry, Pierre Legheraba, Iskander Buecher, Léo Courty, Nicolas Machine Learning Optimization and Control 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 $\mathbb{S}^2$, 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 $\mathcal{O}(n)$ memory and $\mathcal{O}(n^{3/2})$ 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. |
| title | Spherical Harmonic Optimal Transport: Application to Climate Models Comparisons |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2605.18389 |