DecompKAN: Decomposed Patch-KAN for Long-Term Time Series Forecasting

TL;DR

DecompKAN is a lightweight, interpretable time series forecasting model that combines decomposition, patching, normalization, and edge functions, achieving state-of-the-art results on various benchmarks with transparent learned functions.

Contribution

This work introduces DecompKAN, a novel architecture that integrates explicit, visualizable edge functions with decomposition and patching for improved, interpretable long-term time series forecasting.

Findings

Achieves best or tied-best MSE on 15 of 32 dataset-horizon combinations.

Performs best or tied-best on 20 of 36 comparisons across 9 datasets.

Visualization of learned functions reveals domain-specific nonlinearities.

Abstract

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.