WPMixer: Efficient Multi-Resolution Mixing for Long-Term Time Series Forecasting

Full Paper (ARXIV)

---

@inproceedings{murad2025wpmixer,
  title={Wpmixer: Efficient multi-resolution mixing for long-term time series forecasting},
  author={Murad, Md Mahmuddun Nabi and Aktukmak, Mehmet and Yilmaz, Yasin},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={39},
  number={18},
  pages={19581--19588},
  year={2025}
}

🔄 Updates

• [Nov 2025] 🔥🔥🔥 Added full instructions for the optuna hyper-parameter tuning.
• [May 2025] Added a script for hyperparameter tuning using Optuna under ./scripts/HyperParameter_Tuning/. These scripts explore optimal hyperparameter settings for ETT dataset.

Get started

Follow these steps to get started with WPMixer:

1. Install Requirements

Install Python 3.10 and the necessary dependencies.

pip install -r requirements.txt

2. Download Data

Process-1: Download the zip file of the datasets from the link. Paste the zip file inside the root folder and extract. Now you will have ./data/ folder containing all the datasets.

Or, Process-2: Download the data and locate them in the ./data/ folder. You can download all data from the public GitHub repo: Autoformer or TimeMixer. All the datasets are well-pre-processed and can be used easily. To place and rename the datasets file, check the following folder tree,

data
├── electricity
│   └── electricity.csv
├── ETT
│   ├── ETTh1.csv
│   ├── ETTh2.csv
│   ├── ETTm1.csv
│   └── ETTm2.csv
├── exchange_rate
│   └── exchange_rate.csv
├── illness
│   └── national_illness.csv
├── m4
├── solar
│   └── solar_AL.txt
├── traffic
│   └── traffic.csv
└── weather
    └── weather.csv

3. Train the model

We provide the experiment scripts of all benchmarks under the folder ./scripts/ to reproduce the results. Running those scripts by the following commands will generate logs in the ./logs/WPMixer/ folder.

Multivariate long-term forecasting results with full hyperparameter search settings (Table-2):

bash ./scripts/Full_HyperSearch/ETTh1_full_hyp.sh
bash ./scripts/Full_HyperSearch/ETTh2_full_hyp.sh
bash ./scripts/Full_HyperSearch/ETTm1_full_hyp.sh
bash ./scripts/Full_HyperSearch/ETTm2_full_hyp.sh
bash ./scripts/Full_HyperSearch/Weather_full_hyp.sh
bash ./scripts/Full_HyperSearch/Electricity_full_hyp.sh
bash ./scripts/Full_HyperSearch/Traffic_full_hyp.sh

Multivariate long-term forecasting results with unified settings (Table-9 in Supplementary):

bash ./scripts/Unified/ETTh1_Unified_setup.sh
bash ./scripts/Unified/ETTh2_Unified_setup.sh
bash ./scripts/Unified/ETTm1_Unified_setup.sh
bash ./scripts/Unified/ETTm2_Unified_setup.sh
bash ./scripts/Unified/Weather_Unified_setup.sh
bash ./scripts/Unified/Electricity_Unified_setup.sh
bash ./scripts/Unified/Traffic_Unified_setup.sh

Univariate long-term forecasting results (Table-10 in Supplementary):

bash ./scripts/Univariate/ETTh1_univariate.sh
bash ./scripts/Univariate/ETTh2_univariate.sh
bash ./scripts/Univariate/ETTm1_univariate.sh
bash ./scripts/Univariate/ETTm2_univariate.sh

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🔥🔥A. HYPER-PARAMETER TUNING🔥🔥

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Following explains how to run the hyper-tuning scripts for WPMixer, how to organize logs, how to specify datasets, and how each parameter works.

A1. Overview

WPMixer supports automatic hyper-parameter optimization using Optuna. You can run hyper-tuning for one or multiple datasets and automatically search over:

• Learning rates
• Sequence lengths
• Batch size
• Wavelet types
• Decomposition levels
• Patch lengths & strides
• Dropout choices
• Temporal expansion and embedding expansion factors

All results are logged under ./logs/WPMixer/.

A2. Example of the Hyper-parameter Tuning Script:

Following script will also be found in ./scripts/HyperParameter_Tuning/ETT_optuna_unified.sh

if [ ! -d "./logs" ]; then
    mkdir ./logs
fi

if [ ! -d "./logs/WPMixer" ]; then
    mkdir ./logs/WPMixer
fi
export CUDA_VISIBLE_DEVICES=0

# General
model_name=WPMixer
task_name=long_term_forecast

python -u main_run2.py \
	--task_name $task_name \
	--model $model_name \
	--use_hyperParam_optim \
	--datasets ETTh1 ETTh2 \
	--pred_lens 192 \
	--loss smoothL1 \
	--use_amp \
	--n_jobs 1 \
	--optuna_lr 0.00001 0.01 \
	--optuna_batch 128 \
	--optuna_wavelet db2 db3 db5 sym2 sym3 sym4 sym5 coif4 coif5 \
	--optuna_seq_len 96 192 336 \
	--optuna_tfactor 3 5 7 \
	--optuna_dfactor 3 5 7 8 \
	--optuna_epochs 10 \
	--optuna_dropout 0.0 0.05 0.1 0.2 0.4 \
	--optuna_embedding_dropout 0.0 0.05 0.1 0.2 0.4 \
	--optuna_patch_len 16 \
	--optuna_stride 8 \
	--optuna_lradj type3 \
	--optuna_dmodel 128 256 \
	--optuna_weight_decay 0.0 \
	--optuna_patience 5 \
	--optuna_level 1 2 3 \
	--optuna_trial_num 200 >logs/WPMixer/ETTh_192_with_decomposition.log

A3. Parameter Descriptions

This section explains every parameter used in the hyper-tuning script.

General Parameters

Parameter	Description
--task_name	Task type (e.g., long_term_forecast).
--model	Model name (WPMixer).
--loss	Loss function (smoothL1, MSE).
--use_amp	Enables automatic mixed precision for speed.
--datasets	One or multiple datasets to tune together.
--pred_lens	Prediction horizon (e.g., 96).
--n_jobs	Number of parallel Optuna workers.

Optuna Search Space Parameters

Parameter	Description
--optuna_lr lr_min lr_max	Learning rate search interval from minimum LR to max.LR.
--optuna_batch	Candidate batch sizes.
--optuna_wavelet	Wavelet families for multi-resolution decomposition. Set a list of wavelet type to find the optimum one.
--optuna_seq_len	Multiple input sequence lengths to find the optimum one.
--optuna_tfactor	Multiple temporal mixing factors to find the optimum one.
--optuna_dfactor	Multiple embedding mixing factors to find the optimum one.
--optuna_epochs	Max epochs for each trial.
--optuna_dropout	Multiple Dropout search values to find the optimum one.
--optuna_embedding_dropout	Multiple Embedding Dropout search values to find the optimum one.
--optuna_patch_len	Length of each patch.
--optuna_stride	Stride between patches.
--optuna_lradj	Learning rate scheduler policy.
--optuna_dmodel	Multiple embedding dimensions to find the optimum one.
--optuna_weight_decay	Weight decay coefficient for AdamW.
--optuna_patience	Early stopping patience.
--optuna_level	Multiple Wavelet Decomposition levels to find the optimum one.
--optuna_trial_num	Total number of Optuna trials.

⚠️ Note (Important for WPMixer Hyper-Tuning)

When selecting optuna_patch_len and optuna_level, ensure their compatibility with the effective sequence length at the deepest wavelet decomposition branch. If you use $m$ levels in:

--optuna_level m

Then:

• The model uses $m$ detailed resolution branches
• And $1$ approximation branch
• The minimum effective sequence length among all detailed branches becomes: optuna_seq_len / 2^m

To avoid invalid patching, you must satisfy: (optuna_seq_len / 2^m) > optuna_patch_len

Example:

optuna_seq_len = 96
optuna_level = 3   →   effective_seq_len = 96 / 8 = 12
optuna_patch_len = 16   ❌ invalid (12 < 16)

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B. Brief Overview of the Paper

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B1. Abstract:

Time series forecasting is crucial for various applications, such as weather forecasting, power load forecasting, and financial analysis. In recent studies, MLP-mixer models for time series forecasting have been shown as a promising alternative to transformer-based models. However, the performance of these models is still yet to reach its potential. In this paper, we propose Wavelet Patch Mixer (WPMixer), a novel MLP-based model, for long-term time series forecasting, which leverages the benefits of patching, multi-resolution wavelet decomposition, and mixing. Our model is based on three key components: (i) multi-resolution wavelet decomposition, (ii) patching and embedding, and (iii) MLP mixing. Multi-resolution wavelet decomposition efficiently extracts information in both the frequency and time domains. Patching allows the model to capture an extended history with a look-back window and enhances capturing local information while MLP mixing incorporates global information. Our model significantly outperforms state-of-the-art MLP-based and transformer-based models for long-term time series forecasting in a computationally efficient way, demonstrating its efficacy and potential for practical applications.

B2. Model Architecture:

B2. Multivariate Long-Term Forecasting Results with full hyperparameter searching:

B3. Multivariate Long-Term Forecasting under Unified Setting:

B4. Univariate Long-term forecasting result: