Neural operator improves PDE forecasts by refining details across scales
F$^3$NO: Frequency-Decomposed Finite-Time Flow-map Neural Operators with Cross-Scale Conditioning
Machine Learning
Summary
Forecasting complicated systems described by equations can be hard because small details get lost or errors build up over time. The authors created a new method that looks at large patterns first, then uses that to improve the smaller, detailed parts for better predictions. This method also adjusts how it predicts depending on how far into the future it looks, combining short steps for long-term forecasts. Their tests show it makes more accurate predictions than some older methods while using fewer parameters.
What this means in practice
- •For engineering simulation teams: Improve speed and accuracy of simulations for complex physical systems by predicting future states using refined details across different scales.
- •For weather forecasting centers: Enhance weather prediction models by better capturing fine-scale atmospheric patterns without excessive computational cost.
Authors
Fan Wu, Cheng Jing, Kookjin Lee
Abstract
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 recursive propagation between segments. Experiments on five PDE benchmarks demonstrate improved forecasting accuracy over autoregressive and direct-prediction baselines. Ablations show that frequency-decomposed refinement can improve accuracy with fewer parameters, while the benefits of segmentation depend on spatial resolution and dynamical regime.