F$^3$NO：带跨尺度条件的频率分解有限时间流图神经算子

中文摘要 AI 辅助

神经算子可实现快速偏微分方程（PDE）预测，但重复预测会累积误差，且精细尺度结构仍难以解析。我们提出频率分解有限时间流图神经算子（F$^3$NO），其利用更新的低频特征指导高频信息的非线性细化。在每一层内，该跨尺度条件将全局谱处理与局部细节细化相连。模型直接预测指定未来时刻的状态，并根据预测区间调整两个分支的贡献。对于更长轨迹，它将短时间段内的并行预测与段间递归传播相结合。在五个PDE基准上的实验表明，其预测精度优于自回归和直接预测基线。 ablation研究显示，频率分解细化可在更少参数下提升精度，而分段的益处取决于空间分辨率和动力学机制。

英文摘要

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.

发表机构

• Arizona State University（亚利桑那州立大学）

机构由 AI 辅助整理，请以论文原文为准。