MDMLP-EIA: Multi-domain Dynamic MLPs with Energy Invariant Attention for Time Series Forecasting

February 6, 2026 · View on GitHub

arXiv Python 3.8+ PyTorch

This is the official implementation of MDMLP-EIA (Multi-domain Dynamic MLPs with Energy Invariant Attention) for time series forecasting.

Authors: Hu Zhang, Zhien Dai, Zhaohui Tang, Yongfang Xie

Abstract

Time series forecasting is essential across diverse domains. While MLP-based methods have gained attention for achieving Transformer-comparable performance with fewer parameters and better robustness, they face critical limitations including loss of weak seasonal signals, capacity constraints in weight-sharing MLPs, and insufficient channel fusion in channel-independent strategies. To address these challenges, we propose MDMLP-EIA with three key innovations:

  1. Adaptive fused dual-domain seasonal MLP — Categorizes seasonal signals into strong and weak components and employs an adaptive zero-initialized channel fusion (AZCF) strategy to minimize noise interference while effectively integrating predictions.
  2. Energy invariant attention (EIA) — Adaptively focuses on different feature channels within trend and seasonal predictions across time steps while maintaining constant total signal energy to align with the decomposition–prediction–reconstruction framework.
  3. Dynamic capacity adjustment (DCA) — Scales MLP neuron count with the square root of channel count for channel-independent MLPs, ensuring sufficient capacity as channels increase.

Extensive experiments across nine benchmark datasets demonstrate that MDMLP-EIA achieves state-of-the-art performance in both prediction accuracy and computational efficiency.

Environment

  • Python 3.8+
  • PyTorch ≥ 1.7.0
  • CUDA (optional, for GPU training)

Installation

git clone https://github.com/YOUR_USERNAME/MDMLP-EIA.git
cd MDMLP-EIA
pip install -r requirements.txt

Requirements: See requirements.txt. Main dependencies: torch, numpy, pandas, scikit-learn, matplotlib.

Data

Place datasets under ./dataset/ (or set --root_path). Supported datasets:

Quick Start

Training and testing (single run)

python run.py --is_training 1 --model_id ETTh1_96_96 --model MDMLP_EIA --data ETTh1

Citation

If you use this code or the paper in your work, please cite:

@article{zhang2025mdmlp-eia,
  title   = {MDMLP-EIA: Multi-domain Dynamic MLPs with Energy Invariant Attention for Time Series Forecasting},
  author  = {Zhang, Hu and Dai, Zhien and Tang, Zhaohui and Xie, Yongfang},
  journal = {arXiv preprint arXiv:2511.09924},
  year    = {2025},
  url     = {https://arxiv.org/abs/2511.09924}
}

License

This project is for academic use. Please refer to the paper and arXiv for terms of use.