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.
Artificial Intelligence (AI) weather models are improving rapidly, and their forecasts are already competitive with long-established traditional Numerical Weather Prediction (NWP). To build confidence in this new methodology, it is critical that we understand how these predictions are generated. This is a huge challenge as these AI weather models remain largely black boxes. In other areas of Machine Learning (ML), mechanistic interpretability has emerged as a framework for understanding ML predictions by analysing the building blocks responsible for them. Here we present an open-source, highly adaptable tool which incorporates concepts from mechanistic interpretability. The tool organises internal latent representations from the model processor and allows for initial analyses, including cosine similarity and Principal Component Analysis (PCA), enabling the user to identify directions in latent space potentially associated with meteorological features. Applying our tool to the graph neural network GraphCast, we present preliminary case studies for mid-latitude synoptic-scale waves and specific humidity. These demonstrate the tool's ability to identify linear combinations of latent channels that appear to correspond to interpretable features.
Kirsten I. Tempest, Matthias Beylich, George C. Craig
Machine learning weather prediction (MLWP) models have achieved impressive forecasting performance at a small fraction of the computational costs required for traditional physics-based methods. However, they are primarily (1) data-driven and (2) evaluated using pixel-wide error metrics (e.g., RMSE), so there are no guarantees that their forecasts are consistent with known physical laws. We introduce PhysMetrics.Weather, an evaluation framework that assesses the physical realism of MLWP models across three types of metrics: conservation, spectral, and dynamical. By quantifying physical realism, this tool guides the development of physics-informed architectures and helps evaluate whether MLWP models are reliable for operational use. Our framework is available on Github at https://github.com/Emmakast/PhysMetrics.Weather.
While AI weather models excel at short-to-medium range forecasts (up to 15 days), they frequently suffer from ill-defined "instabilities" when rolled out over longer horizons. This work addresses the lack of a formal taxonomy by categorizing these failures into three distinct regimes: blow-up, drift, and loss of seasonality, through year-long rollouts of nine state-of-the-art AI weather models. Our analysis reveals that stability hinges on the treatment of small spatio-temporal scales: unstable models amplify high-frequency energy, while stable models act as denoisers when noise is added to their inputs. Far from reducing these models to mere stochastic parrots, our findings highlight that stable models generate unique weather trajectories, conditioned on the initial state. We verify our findings through ablation studies on architectural design choices, conducted using state-of-the-art Vision Transformer (ViT) AI weather model architectures.