arXiv：cs.LG· Fan Wu, Cheng Jing, Kookjin Lee·· 4 小时前
F³NO：频率分解的有限时间流映射神经算子，带跨尺度条件化
F$^3$NO: Frequency-Decomposed Finite-Time Flow-map Neural Operators with Cross-Scale Conditioning
AI 导读
研究者提出频率分解的有限时间流映射神经算子 F³NO，用更新的低频特征引导高频信息的非线性精修，在每层内通过跨尺度条件化连接全局频谱处理与局部细节精修，并按预测间隔调整两个分支的贡献。在五个 PDE 基准上，F³NO 的预测精度优于自回归与直接预测基线；消融实验显示频率分解精修能以更少参数提升精度，而分段带来的收益取决于空间分辨率与动力学特性。
正文
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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.10998 [cs.LG] |
| (or arXiv:2610.10998v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10998 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Fan Wu [view email]
[v1]
Wed, 7 Oct 2026 23:33:07 UTC (481 KB)
来源：arXiv：cs.LG · arxiv.org