Overview

HADL is a lightweight, PyTorch-based framework for Long-Term Time Series Forecasting (LTSF), optimized for noise robustness, accuracy, and memory efficiency. It integrates Discrete Wavelet Transform (DWT) with a Haar wavelet for noise reduction, Discrete Cosine Transform (DCT) for enhanced feature extraction, and a low-rank layer for efficient, low-parameter forecasting. It is designed to achieve state-of-the-art multivariate forecasting accuracy with minimal trainable parameters, thus offers a computationally efficient solution for long-horizon time series prediction.

Key Features

• Haar Wavelet (DWT): Reduces noise and compresses the input, enabling a lightweight model with fewer parameters.
• Discrete Cosine Transform (DCT): Extracts meaningful long-term patterns.
• Low-Rank Approximation: improve generalization and noise robustness while minimizing memory usage.
• Lightweight Design: A single prediction layer reduces overall complexity, ensuring that the model remains lightweight and interpretable

Usage

Initialization

The model can be initialized with a configuration object that specifies various parameters such as sequence length, prediction length, number of channels, rank for low-rank approximation, and flags to enable/disable Haar, DCT, iDCT and low-rank.

configs = {
    'seq_len': 512,
    'pred_len': 96,
    'enc_in': 7,
    'individual': False,
    'bias': True,
    'enable_Haar': True,
    'enable_DCT': True,
    'enable_iDCT': False,
    'enable_lowrank': True,
    'rank': 30,
}

model = Model(configs)

Configuration Options

Parameter	Description	Default
seq_len	Input sequence length	-
pred_len	Output prediction length	-
enc_in	Number of input features	-
individual	If True, applies a separate layer per feature	False
bias	Enables bias in the low-rank layer	True
enable_Haar	Enables Haar decomposition	True
enable_DCT	Enables Discrete Cosine Transform	True
enable_iDCT	Enables Inverse Discrete Cosine Transform	False
enable_lowrank	Enables Low Rank or Standard Linear Layer	True
rank	Rank of the low-rank layer	30

Forward Pass

The forward method takes an input tensor of shape [Batch, Input length, Channel] and returns an output tensor of shape [Batch, Output length, Channel].

input_tensor = torch.randn(512, 96, 10)  # Example input
output_tensor = model(input_tensor)

Results

Acknowledgement

The listed github repositories have been used for code bases, datasets and comparisons.

• https://github.com/zhouhaoyi/Informer2020
• https://github.com/lss-1138/SparseTSF
• https://github.com/cure-lab/LTSF-Linear
• https://github.com/aikunyi/FreTS
• https://github.com/luodhhh/ModernTCN
• https://github.com/yuqinie98/patchtst
• https://github.com/thuml/iTransformer
• https://github.com/SiriZhang45/FRNet

License

This project is licensed under the MIT License.