PULSE: Generative Phase Evolution for Non-Stationary Time Series Forecasting

Welcome to the official repository of the PULSE paper: "Generative Phase Evolution for Non-Stationary Time Series Forecasting".

Updates

🚩 News (2026.05): PULSE has been accepted to ICML 2026, and the paper and code are currently available.

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Overview

PULSE is a physics-informed framework for non-stationary time series forecasting. It shifts forecasting from passive historical fitting to generative phase evolution, enabling a lightweight backbone to model evolving temporal structures under distribution shifts.

Time series forecasting under non-stationarity requires models to capture stable temporal structures while adapting to future distribution shifts. Existing methods often rely on static assumptions, such as restoring future statistics from historical windows or directly copying historical periodic patterns. These assumptions may cause Phase Amnesia, where models lose awareness of the evolving global temporal context.

PULSE follows a simple design philosophy:

Disentangle → Evolve → Simulate

It contains three key components:

• Phase-Anchored Disentanglement: separates deterministic phase structures from stochastic residual fluctuations.
• Generative Phase Router: generates future phase trajectories instead of rigidly copying historical patterns.
• Statistic-Aware Mixup: simulates residual distribution shifts while avoiding artificial scale collapse.

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Framework

Given a historical sequence, PULSE first constructs a deterministic phase anchor and extracts the residual component:

Historical Input = Phase Anchor + Residual

Unlike standard normalization methods that normalize the raw sequence directly, PULSE normalizes only the stochastic residual while preserving the deterministic phase anchor. The Phase Router then evolves the historical phase anchor into a future-oriented phase anchor, which is injected back during denormalization to reconstruct the final prediction.

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Main Results

PULSE is evaluated on 12 real-world multivariate time series forecasting datasets, covering both long-term and short-term forecasting scenarios.

MSE:   10 / 12 first-place results
MAE:    8 / 12 first-place results
Total: 18 / 24 first-place entries

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Plug-and-Play Capability

PULSE can also be used as a plug-and-play enhancement module for existing forecasting backbones, including DLinear, PatchTST, TimesNet, and iTransformer.

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Ablation Study

The ablation results validate the contribution of each component. Removing the Phase Anchor causes the largest degradation, while removing the Phase Router or Statistic-Aware Mixup also weakens forecasting performance and robustness.

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Phase Evolution Visualization

PULSE does not simply copy historical patterns. Instead, it learns future-oriented phase evolution and maps similar historical anchors to different future phase trajectories when their future dynamics diverge.

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Accuracy--Efficiency Trade-Off

Besides forecasting accuracy, we report actual inference latency and peak GPU memory usage. PULSE improves forecasting accuracy with modest runtime and memory overhead, making it a practical plug-and-play module.

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Requirements

Create the environment with Conda:

conda create -n PULSE python=3.8
conda activate PULSE
pip install -r requirements.txt

Main dependencies:

numpy
matplotlib
pandas
scikit-learn
torch

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Data Preparation

All datasets used in the experiments can be downloaded from:

https://drive.usercontent.google.com/download?id=1l51QsKvQPcqILT3DwfjCgx8Dsg2rpjot&export=download&authuser=0

These datasets are provided by the official iTransformer repository.

After downloading the datasets, create a folder named all_datasets/ in the root directory and place all dataset files directly into this folder.

PULSE/
├── all_datasets/
│   ├── ETTh1.csv
│   ├── ETTh2.csv
│   ├── ETTm1.csv
│   ├── ETTm2.csv
│   ├── electricity.csv
│   ├── traffic.csv
│   ├── weather.csv
│   ├── solar_AL.txt
│   ├── PEMS03.npz
│   ├── PEMS04.npz
│   ├── PEMS07.npz
│   └── PEMS08.npz

Please make sure that the dataset filenames are consistent with the data_path_name specified in each script under scripts/.

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Dataset Summary

Dataset	File Name	Variables	Prediction Lengths	Script
ETTh1	ETTh1.csv	7	96, 192, 336, 720	scripts/ETTh1.sh
ETTh2	ETTh2.csv	7	96, 192, 336, 720	scripts/ETTh2.sh
ETTm1	ETTm1.csv	7	96, 192, 336, 720	scripts/ETTm1.sh
ETTm2	ETTm2.csv	7	96, 192, 336, 720	scripts/ETTm2.sh
Electricity	electricity.csv	321	96, 192, 336, 720	scripts/electricity.sh
Traffic	traffic.csv	862	96, 192, 336, 720	scripts/traffic.sh
Weather	weather.csv	21	96, 192, 336, 720	scripts/Weather.sh
Solar	solar_AL.txt	137	96, 192, 336, 720	scripts/Solar.sh
PEMS03	PEMS03.npz	358	12, 24, 48, 96	scripts/PEMS03.sh
PEMS04	PEMS04.npz	307	12, 24, 48, 96	scripts/PEMS04.sh
PEMS07	PEMS07.npz	883	12, 24, 48, 96	scripts/PEMS07.sh
PEMS08	PEMS08.npz	170	12, 24, 48, 96	scripts/PEMS08.sh

Default setting:

seq_len = 96
metrics = MSE, MAE

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Training

All training scripts are provided in the scripts/ folder.

To reproduce the results on ETTh1, run:

bash ./scripts/ETTh1.sh

To run other datasets:

bash ./scripts/ETTh2.sh
bash ./scripts/ETTm1.sh
bash ./scripts/ETTm2.sh
bash ./scripts/electricity.sh
bash ./scripts/traffic.sh
bash ./scripts/Weather.sh
bash ./scripts/Solar.sh
bash ./scripts/PEMS03.sh
bash ./scripts/PEMS04.sh
bash ./scripts/PEMS07.sh
bash ./scripts/PEMS08.sh

To run all scripts sequentially:

for script in ./scripts/*.sh; do
    bash "$script"
done

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Custom Usage

You can modify the corresponding shell script in scripts/ to customize the dataset, prediction length, batch size, learning rate, and GPU index.

A typical command is:

python -u run.py \
  --is_training 1 \
  --root_path ./all_datasets/ \
  --data_path ETTh1.csv \
  --model PULSE \
  --data ETTh1 \
  --features M \
  --seq_len 96 \
  --pred_len 96 \
  --enc_in 7 \
  --gpu 0

Common arguments:

Argument	Description
--model	Model name, e.g., PULSE
--root_path	Root directory of dataset files
--data_path	Dataset filename
--data	Dataset type
--seq_len	Historical look-back length
--pred_len	Prediction length
--enc_in	Number of input variables
--gpu	GPU index

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Assets

All README figures and tables should be placed under assets/.

assets/
├── fig1_motivation_efficiency.png
├── fig2_framework.png
├── fig3_phase_anchor_visualization.png
├── fig4_plug_and_play_efficiency.png
├── table1_main_results.png
├── table2_plug_and_play.png
├── table3_ablation.png
└── table4_efficiency_tradeoff.png

These files are only used for README visualization and are not required for training or evaluation.

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Citation

If you find this repository useful, please cite our paper:

@inproceedings{liu2026pulse,
  title     = {PULSE: Generative Phase Evolution for Non-Stationary Time Series Forecasting},
  author    = {Liu, Yangyou and Shao, Zezhi and Chen, Xinyu and Chen, Hu and Wang, Fei and Wu, Yuankai},
  booktitle = {Forty-third International Conference on Machine Learning},
  year      = {2026}
}

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Acknowledgement

We sincerely thank the following repositories and benchmark suites for their valuable code bases and datasets:

https://github.com/thuml/iTransformer
https://github.com/thuml/Time-Series-Library
https://github.com/yuqinie98/PatchTST
https://github.com/cure-lab/LTSF-Linear
https://github.com/zhouhaoyi/Informer2020
https://github.com/thuml/Autoformer

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Contact

For questions or discussions, please contact:

Yangyou Liu: 2024223045153@stu.scu.edu.cn