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.

References

The optimal unrolling length for a given PDE and deployment context is not yet understood; more generally, the interplay between training unrolling length and testing rollout horizon remains poorly understood.

— From Numerical Simulators of PDEs to Neural Emulators and Back  (2608.24547 - Koehler, 25 Aug 2026) in Section 10, “Limitations and Open Questions”

HALO remains accurate over the rollout horizons represented during training, but errors accumulate when inference extends substantially beyond that window; reliable long-range forecasting therefore remains an open problem.

— Beyond Pairwise Graphs in Science: Hypergraph Adaptive Wavelet Operators for Parametric PDEs  (2608.27883 - Sarkar et al., 28 Aug 2026) in Section 5, subsection “Limitations and Outlook”