DecompKAN 通过分解与分块实现长时序预测,兼顾高精度与可解释性。
DecompKAN: Decomposed Patch-KAN for Long-Term Time Series Forecasting

- 分趋势残差+通道分块,配合 KAN 神经元学习可可视化函数
- 在 32 组对比中 15 次最优,生理信号数据上优于 iTransformer 10%-17%
- 适合需要透明建模的气候、医疗等科学领域应用
气候建模、生理监测和能源系统等科学领域的精准时间序列预测,既需高预测性能又需模型可解释性。本文提出 DecompKAN,一种轻量级无注意力架构,融合趋势-残差分解、通道式分块、学习型实例归一化及基于 B 样条的科尔莫戈罗夫-阿诺德网络(KAN)边函数。每个 KAN 边学习一个在自学习分块嵌入坐标上的显式、可检查的一维标量函数,可直接可视化。在标准基准测试中,DecompKAN 在 32 个数据集-预测跨度组合中,有 15 组达到或并列最优 MSE;在包含 PPG-DaLiA 生理数据集的 9 个数据集上进行统一训练方案评估时,20/36 次达最优。该模型在具有平滑动态特性的数据(如 Solar -17%、ECL -10% 相较于 iTransformer)和生理时间序列上表现尤为突出。对学习边函数的可视化揭示了不同领域间定性差异的非线性特征。消融实验表明,架构流程(分解、分块、归一化)对性能提升的贡献大于非线性层选择,而 KAN 设计使学习到的潜在变换具备可解释性。
原文摘要 · Abstract (English)
Accurate time series forecasting in scientific domains such as climate modeling, physiological monitoring, and energy systems benefits from both competitive predictions and model transparency. This work proposes DecompKAN, a lightweight attention-free architecture that combines trend-residual decomposition, channel-wise patching, learned instance normalization, and B-spline Kolmogorov-Arnold Network (KAN) edge functions. Each KAN edge learns an explicit, inspectable 1D scalar function over learned patch-embedding coordinates that can be directly visualized. On standard benchmarks, DecompKAN achieves best or tied-best MSE on 15 of 32 dataset-horizon combinations among selected published baselines, and achieves best or tied-best MSE on 20 of 36 comparisons under a controlled same-recipe evaluation across 9 datasets including the physiological PPG-DaLiA benchmark. The architecture shows particular strength on datasets with smooth temporal dynamics (Solar -17%, ECL -10% vs. iTransformer, Weather) and physiological time series. Visualization of learned edge functions reveals qualitatively different latent nonlinearities across domains. Ablation analysis shows that the architectural pipeline (decomposition, patching, normalization) drives performance more than the choice of nonlinear layer, while the KAN formulation enables inspection of learned latent transformations.
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