# The physics of AI weather models

arXiv: https://arxiv.org/abs/2605.23778 · HTML: https://mlsanity.com/paper/2605.23778/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 47 references that are in the map.
- First posted on arXiv 22 May 2026.

## Builds on (most cited first, 23 of 23)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2208.05419/) (2022)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [Sinkformers: Transformers with Doubly Stochastic Attention](https://mlsanity.com/paper/2110.11773/) (2021)
- [A Bayesian Perspective on Generalization and Stochastic Gradient Descent](https://mlsanity.com/paper/1710.06451/) (2017)
- [Skillful joint probabilistic weather forecasting from marginals](https://mlsanity.com/paper/2506.10772/) (2025)
- [FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale](https://mlsanity.com/paper/2507.12144/) (2025)
- [Optimizing Functionals on the Space of Probabilities with Input Convex Neural Networks](https://mlsanity.com/paper/2106.00774/) (2021)
- [A Mathematical Theory of Attention](https://mlsanity.com/paper/2007.02876/) (2020)
- [A Survey on Mechanistic Interpretability for Multi-Modal Foundation Models](https://mlsanity.com/paper/2502.17516/) (2025)
- [The Mean-Field Dynamics of Transformers](https://mlsanity.com/paper/2512.01868/) (2025)
- [A Foundation Model for the Earth System](https://mlsanity.com/paper/2405.13063/) (2024)
- [Universally Converging Representations of Matter Across Scientific Foundation Models](https://mlsanity.com/paper/2512.03750/) (2025)
- [Towards mechanistic understanding in a data-driven weather model: internal activations reveal interpretable physical features](https://mlsanity.com/paper/2512.24440/) (2025)
- [ArchesWeather: An efficient AI weather forecasting model at 1.5deg resolution](https://mlsanity.com/paper/2405.14527/) (2024)
- [Optimal and Diffusion Transports in Machine Learning](https://mlsanity.com/paper/2512.06797/) (2025)
- [FastNet: Improving the physical consistency of machine-learning weather prediction models through loss function design](https://mlsanity.com/paper/2509.17601/) (2025)
- [Mechanistic Interpretability Tool for AI Weather Models](https://mlsanity.com/paper/2604.20467/) (2026)

## Built on by (most cited first, 2 of 2)

- [Missing the Butterfly and Predicting the Past: Features or Bugs of Accurate AI Weather Models?](https://mlsanity.com/paper/2608.25835/) (2026)
- [Stochastically Perturbed Weights: Ensembles from Deterministic Machine-Learning Weather Models](https://mlsanity.com/paper/2609.08412/) (2026)

## Abstract (arXiv)

Could it be that AI weather models are solving physical equations, although they may not be the equations used by conventional NWP models? We compute correlations of forecast skill and Centered Kernel Alignment, providing evidence that different AI weather models represent the atmosphere in similar ways, despite differences in architecture and capacity. We argue that the architecture and training of the AI models constrains the form of the physical laws that they might simulate. In particular, we propose that the models implement a particle description of the atmosphere, where the latent variables at each mesh point correspond to the position of a particle in the high dimensional latent space. We hypothesize that the movement of the particles follows a gradient flow in the latent space towards a minimum of a learned free energy functional. Analysis of the GraphCast and Aurora models show that they make changes on large spatial scales in the early processor layers and move to smaller scale with increasing layer depth, consistent with the gradient flow hypothesis.