Missing the Butterfly and Predicting the Past: Features or Bugs of Accurate AI Weather Models?

AI weather prediction (AIWP) models rival physics-based models, yet the sources of their unexpected forecast accuracy and the degree of their physical fidelity remain unclear. Here, across a hierarchy spanning observation-based reanalysis, a general circulation model, and the multi-scale Lorenz system, we show that AI models can be trained to skillfully predict the past (backcast), though backcasts are systematically less accurate than forecasts. However, skillful backcasting appears to violate the second law of thermodynamics, and all these forecasting and backcasting models miss the butterfly effect. We trace the surprising forecast accuracy, missing butterfly, and skillful backcasting to a single cause: inevitable coarse-graining of training data, which removes fast, small scales and/or some variables. From the Lorenz system to official Pangu-Weather models, reducing coarse-graining makes AI predictions more physics-like (arrow of time and butterfly-like effects emerge), but forecast accuracy declines. Results offer an explanation for AIWP models' forecast skill: unlike physics-based models, they implicitly learn how fast, small scales affect large scales without inheriting their rapid error growth. Broader implications are that AI models' proliferation calls for revisiting predictability theories and long-term climate emulation strategies, and backcasting offers a useful, new lens for such analyses.