F$^3$NO: Frequency-Decomposed Finite-Time Flow-map Neural Operators with Cross-Scale Conditioning
Neural operators enable fast PDE forecasting, but repeated predictions accumulate errors and fine-scale structures remain difficult to resolve. We introduce a frequency-decomposed finite-time flow-map neural operator (F$^3$NO) that leverages updated low-frequency features to guide nonlinear refinement of high-frequency information. Within each layer, this cross-scale conditioning connects global spectral processing with local detail refinement. The model directly predicts states at specified future times and adjusts the contributions of the two branches according to the prediction interval. For longer trajectories, it combines parallel predictions within short temporal segments with recur...
| Authors | Fan Wu, Cheng Jing, Kookjin Lee |
|---|---|
| Primary category | cs.LG |
| Published | 7 October 2026 |
| Last updated at source | 7 October 2026 |
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