Gray Swan Arena in AI Weather Forecasting

• Gray Swan Arena is the analytical space focused on forecasting rare, physically plausible weather extremes that are underrepresented in conventional AI training datasets.
• AI models like FourCastNet demonstrate that excluding extreme events in training leads to significant underestimation of Category 5 tropical cyclones.
• The research emphasizes the need for methodological innovations, such as rare-event resampling and physics-based constraints, to enhance forecast reliability and disaster preparedness.

Gray Swan Arena refers to the analytical and methodological space focused on forecasting “gray swan” weather extremes: events that are possible and physically plausible but so rare that they are essentially absent from training datasets used in contemporary AI weather models. In this context, gray swans are typified by Category 5 tropical cyclones (TCs) that exist outside the distribution of observed events available to machine learning systems during model development. The essential challenge within the Gray Swan Arena is to assess and improve the capacity of AI-based forecasting systems to warn against and characterize the statistics of such out-of-distribution phenomena, whose proper representation is crucial for risk assessment and disaster preparedness.

1. Definition and Scope of Gray Swan Events

Gray swan events, as distinct from “black swans,” refer to rare yet physically possible weather extremes that are not present, or are severely underrepresented, in the observational record used to train AI models. In operational meteorology and climate science, canonical gray swan examples include the most intense tropical cyclones, rare heatwaves, extreme precipitation episodes, and other high-impact phenomena whose return periods far exceed available historical record lengths. The defining operational concern is that standard AI models, trained on the empirical distribution of past weather, may be unable to provide adequate early warning or statistical characterization of these events.

2. Methodological Paradigms for AI Model Training

State-of-the-art AI models for weather prediction, such as FourCastNet (based on the Adaptive Fourier Neural Operator architecture), are typically trained in an autoregressive mode to forecast atmospheric states over fixed intervals (e.g., $x(t + \Delta t) = M(x(t), \theta)$). Training proceeds on large-scale reanalysis datasets (e.g., ERA5, 1979–2015), with global fields and 3D atmospheric variables as inputs. To rigorously probe extrapolation in the Gray Swan Arena, models can be trained under several data regimes, including:

Model Variant	Basin Removal	Extreme Event Exclusion
Full	None	None
Rand	None	None (Random Sample)
noTC	Global	Cat 3–5 TCs
noNA	North Atlantic	Cat 3–5 TCs
noWP	Western Pacific	Cat 3–5 TCs

These model variants are designed to isolate the effect of exposure to the most extreme TCs during training. During training, input noise (zero-mean Gaussian, variance 0.3) is employed for stability. Ensemble forecasting leverages perturbed initial conditions from data assimilation products.

3. Empirical Limits of Extrapolation: Experimental Findings

Empirical evaluation reveals that AI weather models trained without Category 3–5 TCs—such as FourCastNet-noTC—fail to accurately forecast Category 5 events. When evaluated on recent out-of-distribution Category 5 TCs (e.g., Hurricane Lee 2023), models exposed to the full distribution can forecast the characteristic rapid deepening and reduction of minimum sea-level pressure (mslp < 970 hPa). In contrast, FourCastNet-noTC systematically underestimates storm intensity: forecasts remain bounded by the most severe events present in training ($mslp \gtrsim 988$ hPa). Even when initialized with strong out-of-distribution initial conditions, the forecast exhibits a decay toward moderate intensities rather than further intensification.

All model variants—with or without exposure to extremes—exhibit similar skill on globally averaged metrics such as anomaly correlation coefficient (ACC) when tested on “typical” (in-distribution) weather, masking shortcomings for rare extremes. This demonstrates that the physical range learned by the model is set by the span of the training data: extrapolation to the rarest, most impactful cases does not occur.

4. Generalization Across Regional Basins

When Category 3–5 TCs are removed only from specific basins (North Atlantic or Western Pacific) but remain present elsewhere in the training data, generalization is partially restored. FourCastNet-noNA and FourCastNet-noWP, trained on regionally masked data, demonstrate improved skill in forecasting Category 5 TCs within the respective withheld basins, compared to global exclusion. This indicates that knowledge of the fundamental dynamics of extreme TCs, once learned in one basin, can be transferred to others owing to the dynamical similarity of such phenomena (e.g., latent heat processes, convective dynamics). However, the model is unable to generalize from extratropical low-pressure systems to tropical cyclone extremes, highlighting that cross-class extrapolation is constrained by the underlying physical differences.

5. Implications for AI Weather Model Reliability

The inability of models like FourCastNet to extrapolate from weaker to stronger extremes reveals inherent risks for operational deployment. High skill on metrics such as global ACC does not guarantee fidelity in predicting or characterizing the most societally relevant events. As a result, the “interpolation paradigm” sets a practical performance boundary: unless modeling systems are directly or indirectly exposed to the tail of the event distribution, reliable prediction and risk assessment for gray swan weather phenomena remain elusive. In decision-critical environments, this can result in false negatives with potentially catastrophic outcomes.

6. Methodological Innovations and Pathways Forward

Addressing gray swan forecasting requires methodological innovation beyond standard large-scale data assimilation and autocorrelation. Potential approaches include:

• Rare-event sampling and reweighting to emphasize extremes during training.
• Incorporating physics-based constraints, or augmenting training sets with synthetic extremes generated using high-fidelity simulations or generative models that enforce dynamical balance (e.g., via gradient-wind balance: $$g \frac{\partial Z}{\partial r} = \frac{V_g^2}{r} + f V_g$$, with $V_g$ the gradient wind, $Z$ geopotential height, $g$ gravity, $r$ radius, and $f$ the Coriolis parameter).
• Hybrid approaches combining AI with rare-event resampling and data assimilation techniques designed to better capture tail statistics.
• Reformulating loss functions or introducing new training objectives to penalize underperformance on rare, high-impact cases, shifting beyond reliance on global averages.

A plausible implication is that new evaluation metrics—sensitive to both event frequency and impact—will be needed to benchmark gray swan readiness.

7. Broader Context and Future Research Directions

The outlined findings underscore that the Gray Swan Arena is not limited to tropical cyclones. Analogous concerns apply to extremes such as heatwaves, flash floods, severe convective storms, polar vortex collapses, and atmospheric rivers. The question is general: can AI models, armed only with the “typical” training set, extrapolate the physics of rare extremes? Future research in the arena is likely to focus on integrating synthetic and reanalysis datasets, leveraging rare-event simulation algorithms (e.g., large deviation theory), and exploring hybridization of AI and explicit physical constraints. Expanding the distributional tail in training data—by combining ERA5 with long climate integrations—may provide broader coverage, but it does not obviate the need for methodological advances in rare-event learning.

In summary, the Gray Swan Arena delineates a frontier for the evaluation and development of AI-driven weather and climate forecasting systems in anticipating and warning against the rarest and most consequential extremes. Addressing this frontier is essential for the operational reliability of such systems in a changing climate, and demands sustained methodological innovation.