F$^3$NO: Frequency-Decomposed Finite-Time Flow-map Neural Operators with Cross-Scale Conditioning
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.
ProofPaper ↗
Key points
- Neural operators enable fast PDE forecasting, but repeated predictions accumulate errors and fine-scale structures remain difficult to resolve.
- Within each layer, this cross-scale conditioning connects global spectral processing with local detail refinement.
- For longer trajectories, it combines parallel predictions within short temporal segments with recursive propagation between segments.
- Experiments on five PDE benchmarks demonstrate improved forecasting accuracy over autoregressive and direct-prediction baselines.
Sources (1)
- [1]F$^3$NO: Frequency-Decomposed Finite-Time Flow-map Neural Operators with Cross-Scale ConditioningarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 11:33 PM
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.
Neural operators enable fast PDE forecasting, but repeated predictions accumulate errors and fine-scale structures remain difficult to resolve.
Extractive summary: sentences quoted from the sources.