Research map / Time series / Long-term forecasting
WaveletMixer: A Multi-Resolution Wavelets Based MLP-Mixer for Multivariate Long-Term Time Series Forecasting
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes WaveletMixer, which decomposes multivariate time series with multi-level Haar DWT, trains a separate forecaster per wavelet component, iteratively refines them via local and global error propagation, and fuses reconstructions with learnable weights, using an MLP-Mixer backbone (TS-Learner).
Problem
Long-term multivariate time series forecasting, where complex temporal dependencies and multi-scale/frequency patterns are hard to capture with a single prediction model.
Approach
Builds independent learners for each multi-resolution Haar wavelet component (approximation and detail at each level), iteratively aligns them through local (cross-level DWT/IDWT consistency) and global (reconstructed-signal) error propagation, and fuses their reconstructions with learnable weights; the framework is backbone-agnostic and is paired with an MLP-Mixer-based TS-Learner.
Key results
- Across 90 forecasting cases, WaveletMixer achieves 56 best results and reduces average MSE by 7.71% versus iTransformer and 15.15% versus DLinear (averaged over 6 datasets in Table 1).
- Ablation on 5 datasets shows the full initial-local-global training (case 1) gives the best MSE/MAE in all cases, e.g., ETTh1 MSE 0.4102 vs 0.4303 without local phase.
- Applying the MRDWT framework to a Linear model reduces MSE by 30.61% on ETTh2.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the Initial, Local, and Global training phases instead of removing one or more phases (ablation) | WaveletMixer · ETTh1, ETTh2, ETTm1, ETTm2, Weather | MSE | Helped |
| Add the Global phase to Initial + Local training (ablation) | WaveletMixer · ETTh1 | MSE: 0.4303 -> 0.4102 | Helped |
| Add the Local phase to Initial + Global training (ablation) | WaveletMixer · ETTh1 | MSE: 0.4143 -> 0.4102 | Helped |
| Add the Initial phase to Local + Global training (ablation) | WaveletMixer · ETTh1 | MSE: 0.4445 -> 0.4102 | Helped |
| Add the Initial and Local phases to Global-only training (ablation) | WaveletMixer · ETTh1 | MSE: 0.4154 -> 0.4102 | Helped |
| Add the Initial and Global phases to Local-only training (ablation) | WaveletMixer · ETTh1 | MSE: 0.4546 -> 0.4102 | Helped |
| Add the Local and Global phases to Initial-only training (ablation) | WaveletMixer · ETTh1 | MSE: 0.4142 -> 0.4102 | Helped |
| Use learned multi-resolution Fusion instead of Average fusion (ablation) | WaveletMixer · ETTh2, average over H=96, 192, 336, 720 | MSE: 0.344 -> 0.326 | Helped |
| Use learned multi-resolution Fusion instead of Concat fusion (ablation) | WaveletMixer · ETTh2, average over H=96, 192, 336, 720 | MSE: 0.533 -> 0.326 | Helped |
| Use learned multi-resolution Fusion instead of Average fusion (ablation) | WaveletMixer · ETTh2, average over H=96, 192, 336, 720 | MAE: 0.392 -> 0.378 | Helped |
| Use learned multi-resolution Fusion instead of Concat fusion (ablation) | WaveletMixer · ETTh2, average over H=96, 192, 336, 720 | MAE: 0.495 -> 0.378 | Helped |
| Add high-frequency components to the predictions (ablation) | WaveletMixer · 6 studied datasets | MSE: up to 23.4% | Helped |
Surprising findings
- Concatenating predictions instead of learnable fusion degrades ETTh2 MSE sharply at long horizons (0.871 vs 0.376 at H=720 for average fusion in Table 3).
Limitations
- Evaluated only with Haar wavelets as the main basis; other wavelet bases are left to future work and only briefly compared on ETTh1.
- Ablation and sensitivity analyses are largely deferred to supplementary material; the main text reports averaged results on 6 of 9 datasets.
- Gains over strongest baselines are mixed (56 of 90 cases best), and mr-Diff is only compared on MAE.
Experimental setup
Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Weather Electricity Traffic Exchange ILI
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 Exchange Electricity Weather Traffic ILI
Metrics: MSE MAE
Baselines: iTransformer TimeMixer TSMixer PatchTST TimesNet Crossformer DLinear MICN FiLM NSformer FEDformer Pyraformer
Builds on: MLP-Mixer RevIN PatchTST DLinear MRDWT
Closest papers by meaning
- WPMixer: Efficient Multi-Resolution Mixing for Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.94)
- Enhancing Foundation Models for Time Series Forecasting via Wavelet-based Tokenization (ICML 2025 · similarity 0.90)
- xLSTM-Mixer: Multivariate Time Series Forecasting by Mixing via Scalar Memories (NeurIPS 2025 · similarity 0.89)
- TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting (ICLR 2024 · similarity 0.89)
- HDMixer: Hierarchical Dependency with Extendable Patch for Multivariate Time Series Forecasting (AAAI 2024 · similarity 0.88)
- Adaptive Multi-Scale Decomposition Framework for Time Series Forecasting (AAAI 2025 · similarity 0.87)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.