Wind Power Forecasting with Mamba and DMD

Overview

A hybrid forecasting framework combining deep sequence modeling with physics-inspired error correction for wind power prediction. The model uses a dual-branch architecture to extract features from historical and future data separately, fuses them into a unified representation, and employs a Mamba block for efficient global dependency modeling. Predictions are further refined through Dynamic Mode Decomposition (DMD)-based residual correction.

Key contributions:

• Dual-Branch Context Encoding: A parallel TCN and 1D-ResNet architecture separately encodes historical power trajectories and future meteorological signals, providing task-aligned local representations before fusion.
• Efficient Long-Range Modeling: A Mamba-based encoder models global temporal dependencies and cross-variable interactions with linear complexity O(L).
• Dynamic Residual Correction: DMD is introduced to model structured residual dynamics and correct systematic forecast bias under non-stationary conditions.

Architecture

Historical Features (X1)          Future Features (X2)
        │                                │
        ▼                                ▼
  ┌──────────┐                    ┌──────────┐
  │   TCN    │                    │  ResNet  │
  │ (dilated │                    │ (1D, 7×7 │
  │  causal, │                    │  + pool) │
  │  resnet) │                    │          │
  └────┬─────┘                    └────┬─────┘
       │                               │
       ▼                               │
  ┌──────────┐                         │
  │  Mamba   │                         │
  │  Block   │                         │
  └────┬─────┘                         │
       │                               │
       ▼                               │
  ┌──────────┐                         │
  │ Temporal │                         │
  │ Attention│                         │
  └────┬─────┘                         │
       │                               │
       └───────────┬───────────────────┘
                   │
                   ▼
            ┌────────────┐
            │  Concat +  │
            │ Task Heads │
            └─────┬──────┘
                  │
           ┌──────┴──────┐
           ▼             ▼
     ROUND(A.POWER,0)   YD15
                  │
                  ▼
           ┌────────────┐
           │ DMD-based  │
           │ Correction │
           └────────────┘

Project Structure

Windpower_prediction/
├── model/
│   ├── models.py          # Model definitions (MultiTaskModel, TCNResBlock, MambaBlock, ResNet, etc.)
│   ├── dataloader.py      # Dataset class with sliding window and Z-score normalization
│   ├── dataset.py         # Data preprocessing and cyclical feature engineering
│   ├── train.py           # Main training pipeline with DMD correction
│   ├── train_ablation.py  # Ablation study scripts (baseline/dmd/fusion/full)
│   └── utils.py           # DMD decomposition and Hankel matrix utilities
├── data/                  # Turbine CSV files (11.csv ~ 20.csv)
└── output/
    ├── checkpoints/       # Per-turbine model weights (turbine_14.pth, etc.)
    ├── scaler/            # Per-turbine StandardScaler pkl files
    ├── plots/             # Prediction visualization PNGs
    └── metrics/           # Per-horizon evaluation CSVs (ablation mode)

Installation

Requirements:

• Python 3.10+
• PyTorch 2.0+ (with CUDA)
• mamba-ssm
• scikit-learn, pandas, numpy, matplotlib, tqdm, joblib

# Create conda environment
conda create -n windpower python=3.12
conda activate windpower

# Install PyTorch (adjust CUDA version as needed)
pip install torch --index-url https://download.pytorch.org/whl/cu128

# Install mamba-ssm (requires CUDA toolkit)
pip install causal-conv1d mamba-ssm

# Install other dependencies
pip install scikit-learn pandas numpy matplotlib tqdm joblib

Alternatively, install all dependencies from requirements.txt:

pip install -r requirements.txt

Usage

Data Preparation

Place turbine CSV files in the data/ directory. Each file should be named {turbine_id}.csv with the following columns:

Column	Description
DATATIME	Timestamp (15-min intervals)
WINDSPEED	Numerical weather prediction wind speed
PREPOWER	Previous period cumulative power
WINDDIRECTION	Wind direction
TEMPERATURE	Ambient temperature
HUMIDITY	Relative humidity
PRESSURE	Atmospheric pressure
ROUND(A.WS,1)	Measured wind speed
ROUND(A.POWER,0)	Measured active power (target 1)
YD15	YD15 power indicator (target 2)

Training

cd model

# Full training (all turbines)
python train.py

# Ablation studies with different modes
python train_ablation.py --mode baseline    # TCN+Mamba only, no fusion, no DMD
python train_ablation.py --mode dmd         # TCN+Mamba + DMD correction
python train_ablation.py --mode fusion      # TCN+Mamba + ResNet future feature fusion
python train_ablation.py --mode full        # TCN+Mamba + fusion + DMD

# Single turbine with custom hyperparameters
python train_ablation.py --mode full --turbine 14 --epochs 30 --batch 64 --lr 0.0005

Hyperparameter Search

# Bayesian optimization with Optuna (searches lr, mamba_hidden, tcn_channels, huber_delta)
python search.py --trials 20 --turbine 14 --epochs 20

Results are saved to output/metrics/search_turbine_{id}.csv.

Hyperparameters

Parameter	Value	Description
Input window L	480 steps	5 days of historical data
Prediction horizon H	96 steps	24 hours forecast
Stride	76 steps	Sliding window stride
Batch size	128
Learning rate	0.00164	Adam optimizer (beta1=0.5, beta2=0.999)
Gradient clipping	max_norm=0.5	Prevents numerical instability
Early stopping patience	10 epochs
Train / Val / Test split	70% / 20% / 10%	Chronological split
DMD Hankel window K	20
Dropout	0.2	Applied to TCN, ResNet, Mamba, task heads
Huber loss delta	1.36
Mamba hidden dim	128
TCN channels	[64, 128, 256]
Loss weight ωt	0.1 → 0.5	Linear increase over training

Model Components

Component	Description	File
MultiTaskModel	Full model: TCN → Mamba → Attention → ResNet fusion → dual heads	models.py
TCNResBlock	Dilated causal convolution with residual connection	models.py
MambaBlock	Positional encoding + stacked Mamba SSM layers	models.py
TemporalAttention	Tanh-based temporal attention over Mamba outputs	models.py
ResNet	1D-ResNet encoding future meteorological features	models.py
DynamicWeightedLoss	Epoch-dependent weighted Huber loss (ωt: 0.1→0.5)	models.py
EarlyStopping	Per-turbine checkpoint saving with NaN detection	models.py

Evaluation Metrics

• RMSE: Root Mean Squared Error
• MAE: Mean Absolute Error
• ACC-NRMSE: 1 - NRMSE (Accuracy of Normalized RMSE)
• ACC-NMAE: 1 - NMAE (Accuracy of Normalized MAE)
• R²: Coefficient of Determination

License

This project is licensed under the MIT License. See LICENSE for details.