Spherical Harmonic Optimal Transport: Application to Climate Models Comparisons

2026-05-18 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

A new framework, Spherical Harmonic Optimal Transport (SHOT), has been developed to compare measures on the 2-sphere ($\mathbb{S}^2$) with significantly reduced computational cost compared to traditional optimal transport methods. This approach leverages convolutional algorithms based on the heat kernel, demonstrating that the heat kernel cost converges to the optimal transport cost as time vanishes for both balanced and unbalanced cases. SHOT ensures that its associated Sinkhorn divergences maintain the geometric and analytic properties of classical optimal transport. By utilizing the harmonic structure of the sphere, the framework achieves a fast Sinkhorn algorithm requiring only $\mathcal{O}(n)$ memory and $\mathcal{O}(n^{3/2})$ time per iteration, with GPU-friendly operations. This computational efficiency is validated on synthetic data, and the method shows promise for evaluating global climate models, offering spatial and seasonal performance insights.

Key takeaway

For climate scientists and researchers comparing complex geospatial datasets, SHOT offers a computationally efficient and theoretically sound alternative to traditional optimal transport. You can gain detailed spatial and seasonal insights into model performance without incurring prohibitive computational costs. Consider integrating SHOT into your model evaluation pipelines to enhance analysis speed and depth, especially for large-scale spherical data.

Key insights

Spherical Harmonic Optimal Transport (SHOT) efficiently compares measures on a sphere, retaining geometric properties.

Principles

• Heat kernel cost converges to optimal transport cost.
• Harmonic structure enables fast Sinkhorn algorithms.

Method

The method uses heat kernel-based convolutional algorithms on the 2-sphere, leveraging its harmonic structure to derive a fast Sinkhorn algorithm with $\mathcal{O}(n)$ memory and $\mathcal{O}(n^{3/2})$ time per iteration.

In practice

• Compare global climate models.
• Analyze spatial and seasonal model performance.

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.