PhysMetrics.Weather: An Evaluation Framework for Physical Consistency in ML Weather Models

Despite their high accuracy on point-wise metrics, machine learning weather forecasting models can exhibit different failure modes such as blurring, periodic irregularities, and other unphysical spatial artifacts. This has motivated a variety of metrics to detect known failure cases. Existing metrics fix a representation or transformation in advance, and that choice limits the artifacts they can detect. We propose to train a discriminator for separating reference data from the model's output, and using its output logit to obtain a divergence-like realism score. The discriminator learns whatever separates the model's fields from real weather, adapting to whichever failure mode that model exhibits. We compare our learned atmospheric critic to existing metrics using various synthetic corruptions applied to ERA5 reanalysis data. Our method successfully identifies the corruptions and ranks their severity, while existing metrics fail on at least one corruption. Additionally, we evaluate forecasts from real weather models, and find that the realism score degrades with longer lead times and the metric generally assigns higher realism to numerical models than to machine learning models.

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.

Multivariate forecasting in physical systems requires models that predict coupled temporal variables while preserving meaningful state evolution. Deep forecasters can fit temporal correlations, and physics-informed models can regularize predictions with scientific constraints, but these directions are often connected only at the decoded-output level. As a result, the hidden predictive state that generates future trajectories may remain statistically useful but physically unstructured. We introduce Phys-JEPA, a physics-informed joint-embedding predictive architecture for multivariate time-series forecasting. Phys-JEPA learns a latent world model in which predictive states are decomposed into physical and residual components, and physical consistency is imposed directly on latent states and latent transitions rather than only on decoded forecasts. This formulation uses known physical variables to organize the representation space while retaining residual capacity for unresolved dynamics. On Jena Climate 2009--2016, Phys-JEPA reduces aggregate MSE from 0.12482 to 0.12273 and temperature MSE from 0.01892 to 0.01831 at H=24. On Traffic, full Phys-JEPA improves aggregate MSE over the supervised baseline across all tested horizons, reducing H=192 MSE from 0.800784 to 0.773873. On Electricity, the best variant depends on horizon: static latent consistency is strongest at H=24 and H=48, while full Phys-JEPA gives the best aggregate and target-variable MSE at H=192. These initial results suggest that moving physics-informed learning from output space to latent predictive state space is a promising direction for interpretable temporal world models.