[2604.01215] The Recipe Matters More Than the Kitchen:Mathematical Foundations of the AI Weather Prediction Pipeline

Computer Science > Machine Learning arXiv:2604.01215 (cs) [Submitted on 1 Apr 2026] Title:The Recipe Matters More Than the Kitchen:Mathematical Foundations of the AI Weather Prediction Pipeline Authors:Piyush Garg, Diana R. Gergel, Andrew E. Shao, Galen J. Yacalis View a PDF of the paper titled The Recipe Matters More Than the Kitchen:Mathematical Foundations of the AI Weather Prediction Pipeline, by Piyush Garg and 3 other authors View PDF HTML (experimental) Abstract:AI weather prediction has advanced rapidly, yet no unified mathematical framework explains what determines forecast skill. Existing theory addresses specific architectural choices rather than the learning pipeline as a whole, while operational evidence from 2023-2026 demonstrates that training methodology, loss function design, and data diversity matter at least as much as architecture selection. This paper makes two interleaved contributions. Theoretically, we construct a framework rooted in approximation theory on the sphere, dynamical systems theory, information theory, and statistical learning theory that treats the complete learning pipeline (architecture, loss function, training strategy, data distribution) rather than architecture alone. We establish a Learning Pipeline Error Decomposition showing that estimation error (loss- and data-dependent) dominates approximation error (architecture-dependent) at current scales. We develop a Loss Function Spectral Theory formalizing MSE-induced spectral blurring...