Why Directly Learning Periodic Trajectories Can Fail
Operator learning of periodic solutions requires deciding how simulation data should be recorded and represented. A natural choice is to integrate long enough for transients to decay and record a window wide enough to contain at least one full period of all trajectories. We find that these conservative choices can make the resulting trajectories difficult to learn, even when the underlying periodic orbits vary regularly with system parameters. Unaligned trajectories generalize poorly even within the training distribution. Phase alignment substantially improves in-distribution generalization, but models trained on a fixed physical-time window still have large errors on trajectories with pe...
| Authors | Kaixin Zheng, Anita Layton |
|---|---|
| Primary category | cs.AI |
| Published | 26 September 2026 |
| Last updated at source | 26 September 2026 |
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