Optimal autoregressive training and testing horizons

Determine the optimal unrolling length for a given partial differential equation and deployment context, and characterize the relationship between training unrolling length and testing rollout horizon.

Background

Autoregressive neural emulators are trained by applying the learned map for one or more steps and are evaluated over potentially much longer rollouts. Increasing the training unrolling length can expose the model to its own prediction errors, but also increases computational and optimization costs.

The thesis explicitly states that neither the best training unrolling length nor its relationship to the deployment horizon is understood. Resolving this would guide the selection of training configurations in APEBench and related emulator systems.