Research map / Time series / Long-term forecasting
Adaptive Multi-Scale Decomposition Framework for Time Series Forecasting
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Proposes AMD, an MLP-based time series forecaster that decomposes input into multi-scale temporal patterns via average downsampling, models temporal and channel dependencies, and adaptively synthesizes predictions with a dense mixture-of-experts selector.
Problem
Long- and short-term time series forecasting where patterns at multiple overlapping scales are entangled, while Transformers are costly and overfit and simple MLPs lack capacity to capture complex multi-scale patterns.
Approach
Decompose the series into multi-scale temporal patterns through average-pooling downsampling and residual mixing (MDM), model temporal and cross-channel dependencies with a scaled dual-dependency MLP block (DDI), and combine per-scale predictors with input-dependent gating weights (AMS) instead of simple averaging as in TimeMixer.
Key results
- AMD achieves best MSE/MAE in 50 of 80 long-term cases and second-best in 27 of 80 cases across long-term benchmarks.
- On PEMS short-term forecasting (input 96, horizon 12), AMD attains best MSE on all four PEMS datasets, e.g., 0.084 on PEMS03 versus 0.085 for TimesNet.
- Adding MDM and AMS to DLinear improves average MSE by 6.46% on Weather and 1.41% on ECL.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add multi-scale decomposition and adaptive synthesis to DLinear | DLinear · Weather | MSE: 6.46% | Helped |
| Add multi-scale decomposition and adaptive synthesis to MTS-Mixers | MTS-Mixers · Weather | MSE: 1.38% | Helped |
| Use sparse MoE instead of dense MoE (ablation) | AMD · Weather and ECL | MSE: 0.145 -> 0.150 | Hurt |
| Replace temporal pattern order with random order (ablation) | AMD · Weather and ECL | MSE: 0.145 -> 0.152 | Hurt |
| Replace TP-Selector with average weighting (ablation) | AMD · Weather and ECL | MSE: 0.145 -> 0.149 | Hurt |
| Remove DDI (ablation) | AMD · Weather and ECL | MSE: 0.145 -> 0.154 | Hurt |
| Set DDI scaling rate β to 0.5 (ablation) | AMD · Weather and ECL | MSE: 0.145 -> 0.146 | Mixed |
| Set DDI scaling rate β to 1.0 (ablation) | AMD · Weather and ECL | MSE: 0.145 -> 0.147 | Hurt |
| Remove selector loss (ablation) | AMD · Weather and ECL | MSE: 0.145 -> 0.160 | Hurt |
| Remove MDM (ablation) | AMD · Weather and ECL | MSE: 0.145 -> 0.149 | Hurt |
| Remove AMS and use a single linear predictor (ablation) | AMD · Weather and ECL | MSE: 0.145 -> 0.150 | Hurt |
Surprising findings
- Adding cross-channel dependencies (beta=0.5 or 1.0) does not consistently improve accuracy, indicating channel mixing can introduce noise on weakly correlated datasets.
- Sparse top-k MoE in the projection stage yields higher errors than the dense MoE variant, suggesting omitting non-dominant patterns hurts performance.
Limitations
- Relies on the availability and quality of historical data, which may be challenging with limited or noisy data.
- Cross-channel dependencies can distort the target distribution and need a tuned scaling rate beta.
- Efficiency gains are reported only on Weather with the official configurations; the paper acknowledges open issues such as distribution shift in deep layers.
Experimental setup
Datasets: Weather ETTh1 ETTh2 ETTm1 ETTm2 ECL Exchange Traffic Solar-Energy PEMS03 PEMS04 PEMS07
Benchmarks: Weather ETTh1 ETTh2 ETTm1 ETTm2 ECL Exchange Traffic Solar-Energy PEMS03 PEMS04 PEMS07
Metrics: MSE MAE
Baselines: TimeMixer TiDE MTS-Mixers RLinear DLinear PatchTST iTransformer Crossformer FEDformer TimesNet MICN
Builds on: TimeMixer DLinear MTS-Mixers noisy top-k gating RevIN
Closest papers by meaning
- TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting (ICLR 2024 · similarity 0.90)
- Unlocking the Power of Patch: Patch-Based MLP for Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.88)
- Time-MMD: Multi-Domain Multimodal Dataset for Time Series Analysis (NeurIPS 2024 · similarity 0.88)
- Multi-Scale Finetuning for Encoder-based Time Series Foundation Models (NeurIPS 2025 · similarity 0.88)
- TimeEmb: A Lightweight Static-Dynamic Disentanglement Framework for Time Series Forecasting (NeurIPS 2025 · similarity 0.88)
- WPMixer: Efficient Multi-Resolution Mixing for Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.87)
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