HaKAN

Time Series Forecasting with Hahn Kolmogorov-Arnold Networks

This repository contains the code for our project on long-term time series forecasting.

Architecture

The model integrates channel independence, reversible instance normalization, and patching, followed by patch and position embeddings. A stack of R Hahn-KAN blocks, each with intra-patch and inter-patch KAN layers using Hahn polynomials, processes the embedded sequence to capture temporal patterns. The output is mapped through a bottleneck structure with two fully connected layers to produce the final forecast.

📊 Long-term Forecasting Results (Avg. MSE, MAE)

Look-back = 96, averaged over T ∈ {96, 192, 336, 720}
Lower is better.

Dataset	HaKAN	S-Mamba	iTrans	RLinear	PatchTST	Crossf.	TiDE	TimesNet	FEDformer
ETTh1	0.439 (0.429)	0.455 (0.450)	0.454 (0.447)	0.446 (0.434)	0.469 (0.454)	0.529 (0.522)	0.541 (0.507)	0.458 (0.450)	0.440 (0.460)
ETTh2	0.348 (0.383)	0.381 (0.405)	0.383 (0.407)	0.374 (0.398)	0.387 (0.407)	0.942 (0.684)	0.611 (0.550)	0.414 (0.427)	0.437 (0.449)
ETTm1	0.384 (0.399)	0.398 (0.405)	0.407 (0.410)	0.414 (0.407)	0.387 (0.400)	0.513 (0.496)	0.419 (0.419)	0.400 (0.406)	0.448 (0.452)
ETTm2	0.276 (0.324)	0.288 (0.332)	0.288 (0.332)	0.286 (0.327)	0.281 (0.326)	0.757 (0.610)	0.358 (0.404)	0.291 (0.333)	0.305 (0.349)

📌 Format: MSE (MAE).

Requirements

pip install numpy==1.24.3 matplotlib==3.7.2 pandas==2.0.3 scikit-learn==1.3.0 torch==2.4.1+cu121 

Datasets

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The datasets are hosted on Google Drive by Autoformer. Please download them and place them in the ./datasets/ directory before running the experiments.

👉 Access the Datasets on Google Drive

Experiments

If you want to run an experiment, just run the following script and edit it as you need. This script is for the look-back window is 96.

sh ./scripts/SHORT/etth1.sh

If you want to run an experiment for the look-back window 336, you should run the following script:

sh ./scripts/LONG/etth1.sh

🙏 Acknowledgements

We gratefully acknowledge the following repositories and authors whose work inspired or supported our research:

• 🔗 ZimingLiu/Kolmogorov-Arnold-Network
  Provided the foundational implementation of Kolmogorov-Arnold Networks (KANs).

• 🧠 YuqiNie/PatchTST
  Served as a strong baseline for comparison in multivariate time series forecasting.

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We appreciate the open-source contributions that helped make this work possible.

📄 Citation

If you use this work, please cite:

@inproceedings{Hasanetal-2026-HaKAN,
  title     = {HaKAN: Time Series Forecasting with Hahn Kolmogorov-Arnold Networks},
  author    = {Hasan, Md Zahidul and
               Ben Hamza, Abdessamad and
               Bouguila, Nizar},
  booktitle = {Proceedings of the International Conference on Artificial Intelligence and Statistics},
  year      = {2026}
}