# TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting

arXiv: https://arxiv.org/abs/2502.06910 · HTML: https://mlsanity.com/paper/2502.06910/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 32 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 21 of 21)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting](https://mlsanity.com/paper/2205.08897/) (2022)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [Convolutional Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.13155/) (2024)

## Built on by (most cited first, 30 of 30)

- [Enhancing Time Series Forecasting through Selective Representation Spaces: A Patch Perspective](https://mlsanity.com/paper/2510.14510/) (2025)
- [GCGNet: Graph-Consistent Generative Network for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2603.08032/) (2026)
- [Learning with Calibration: Exploring Test-Time Computing of Spatio-Temporal Forecasting](https://mlsanity.com/paper/2506.00635/) (2025)
- [Gated QKAN-FWP: Scalable Quantum-inspired Sequence Learning](https://mlsanity.com/paper/2605.06734/) (2026)
- [TFKAN: Time-Frequency KAN for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2506.12696/) (2025)
- [SynTSBench: Rethinking Temporal Pattern Learning in Deep Learning Models for Time Series](https://mlsanity.com/paper/2510.20273/) (2025)
- [LoFT-LLM: Low-Frequency Time-Series Forecasting with Large Language Models](https://mlsanity.com/paper/2512.20002/) (2025)
- [PHAT: Modeling Period Heterogeneity for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2602.00654/) (2026)
- [How (Not) to Hybridize Neural and Mechanistic Models for Epidemiological Forecasting](https://mlsanity.com/paper/2602.06323/) (2026)
- [How Effective Are Time-Series Models for Precipitation Nowcasting? A Comprehensive Benchmark for GNSS-based Precipitation Nowcasting](https://mlsanity.com/paper/2509.25263/) (2025)
- [Time series forecasting with Hahn Kolmogorov-Arnold networks](https://mlsanity.com/paper/2601.18837/) (2026)
- [Prior Knowledge-enhanced Spatio-temporal Epidemic Forecasting](https://mlsanity.com/paper/2602.22270/) (2026)
- [TimeAPN: Adaptive Amplitude-Phase Non-Stationarity Normalization for Time Series Forecasting](https://mlsanity.com/paper/2603.17436/) (2026)
- [DecompKAN: Decomposed Patch-KAN for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2604.23968/) (2026)
- [Learning Intrinsic Water-Quality Dynamics with Rainfall for Data-Driven Forecasting](https://mlsanity.com/paper/2508.08279/) (2025)
- [Echo Flow Networks](https://mlsanity.com/paper/2509.24122/) (2025)
- [OmniFuser: Adaptive Multimodal Fusion for Service-Oriented Predictive Maintenance](https://mlsanity.com/paper/2511.01320/) (2025)
- [Multi-Modal Scene Graph with Kolmogorov-Arnold Experts for Audio-Visual Question Answering](https://mlsanity.com/paper/2511.23304/) (2025)
- [Temporal Functional Circuits: From Spline Plots to Faithful Explanations in KAN Forecasting](https://mlsanity.com/paper/2605.05685/) (2026)
- [VLBM: Variational Latent Basis Modeling for OOD Robust Multivariate Time Series Forecasting](https://mlsanity.com/paper/2606.02138/) (2026)
- [Multiple cyclicity and Wavelet Decomposition with Channel Correlation for Long-term Time Series Forecasting](https://mlsanity.com/paper/2606.17996/) (2026)
- [Complementary Matrix-Gated QKAN Fast-Weight Programmers for Quantum Dynamics Forecasting](https://mlsanity.com/paper/2607.27945/) (2026)
- [AirFlow: Context Preserving and Multi-Rate State Modeling for Air Quality Forecasting](https://mlsanity.com/paper/2608.09775/) (2026)
- [PGP-Clinical-TimeKAN: Prior-Guided Joint Probabilistic Forecasting of Clinical Trajectories](https://mlsanity.com/paper/2609.05488/) (2026)
- [HypLTSF: A Hyperbolic Geometric View of Multi-Scale Hierarchies for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2609.08286/) (2026)
- [WorldTS: World Modeling for Multimodal Covariate-aware Time Series Forecasting](https://mlsanity.com/paper/2609.31162/) (2026)
- [XMatch: Enhancing Covariate-Aware Time Series Forecasting through Tree-Structured Exogenous Matching](https://mlsanity.com/paper/2609.34939/) (2026)
- [Dual-Context Analog Retrieval for Time Series Forecasting](https://mlsanity.com/paper/2610.03491/) (2026)
- [Most-Recent Anchoring with Recurrent Ordering for Time Series Forecasting](https://mlsanity.com/paper/2610.03494/) (2026)
- [FreSia: Frequency-Semantic Instantiation and Alignment for Multivariate Time Series Analysis](https://mlsanity.com/paper/2610.05726/) (2026)

## Abstract (arXiv)

Real-world time series often have multiple frequency components that are intertwined with each other, making accurate time series forecasting challenging. Decomposing the mixed frequency components into multiple single frequency components is a natural choice. However, the information density of patterns varies across different frequencies, and employing a uniform modeling approach for different frequency components can lead to inaccurate characterization. To address this challenges, inspired by the flexibility of the recent Kolmogorov-Arnold Network (KAN), we propose a KAN-based Frequency Decomposition Learning architecture (TimeKAN) to address the complex forecasting challenges caused by multiple frequency mixtures. Specifically, TimeKAN mainly consists of three components: Cascaded Frequency Decomposition (CFD) blocks, Multi-order KAN Representation Learning (M-KAN) blocks and Frequency Mixing blocks. CFD blocks adopt a bottom-up cascading approach to obtain series representations for each frequency band. Benefiting from the high flexibility of KAN, we design a novel M-KAN block to learn and represent specific temporal patterns within each frequency band. Finally, Frequency Mixing blocks is used to recombine the frequency bands into the original format. Extensive experimental results across multiple real-world time series datasets demonstrate that TimeKAN achieves state-of-the-art performance as an extremely lightweight architecture. Code is available at https://github.com/huangst21/TimeKAN.