Autoregressive Rollout
Definition
Feeding a trained one-step model its own predictions repeatedly to advance many time steps. It is the standard way to do temporal field prediction and the main source of error accumulation.
What it is
The model is trained for a single step, u(t) -> u(t+dt). At inference you feed the predicted u(t+dt) back in and march forward step by step to step N. One short-horizon model thus produces a long forecast.
Key points
- Error accumulation is fundamental: even 1% single-step error can completely derail 100 steps, and the deviation typically grows exponentially.
- Standard mitigations: multi-step loss during training (the pushforward trick), noise injection for robustness, and coarse-grained rollouts with larger time steps.
- Distribution drift: as the rollout proceeds, inputs leave the training distribution and the model enters states it has never seen, accelerating error growth.
- Evaluation must report an error curve versus rollout step; single-step error alone badly overstates capability.
Common pitfalls / boundaries
- High single-step accuracy does not mean long-term stability. Select models by "usable rollout horizon", not single-step error.
- Models that violate energy/mass conservation drift out of the physically feasible region over long rollouts; add conservation constraints or periodically correct with observations (data assimilation).