CAST-Norm

This is an official implementation of paper: [CAST-Norm: Coupled Adaptive Spatio-Temporal Normalization for Multivariate Time Series Forecasting](KDD 2026). CAST-Norm is a normalization framework for time series forecasting that addresses non-stationarity through spatial-temporal coupling perception and community-aware spatial purification.

Modules

• Temporal Normalization: Normalizes time series along the temporal dimension
• Spatial-Temporal Coupling Perception (STCP): Captures dynamic spatial-temporal relationships via patch-wise graph learning
• Community-Aware Spatial Purification (CASD): Separates invariant and variant patterns using community detection
• Coupling-Aware Recalibration: Restores forecasts to original scale using learned coupling relationships

Installation

pip install torch numpy pandas scikit-learn

For S_Mamba model:

pip install mamba-ssm

Quick Start

Training

python run.py \
    --task_name long_term_forecast \
    --is_training 1 \
    --model_id ETTh1_informer_castnorm_96_96 \
    --model Informer \
    --data ETTh1 \
    --root_path ./data/ETT/ \
    --data_path ETTh1.csv \
    --features M \
    --freq h \
    --seq_len 96 \
    --label_len 48 \
    --pred_len 96 \
    --enc_in 7 \
    --dec_in 7 \
    --c_out 7 \
    --d_model 512 \
    --n_heads 8 \
    --e_layers 2 \
    --d_layers 1 \
    --d_ff 2048 \
    --dropout 0.1 \
    --norm_type CAST-Norm \
    --cast_norm_denorm recalib \
    --enable_stcp \
    --enable_casd \
    --lambda1 1.0 \
    --lambda2 1.0 \
    --train_epochs 10 \
    --batch_size 32 \
    --learning_rate 0.0001

Testing

python run.py \
    --task_name long_term_forecast \
    --is_training 0 \
    --model_id ETTh1_informer_castnorm_96_96 \
    --model Informer \
    --data ETTh1 \
    --root_path ./data/ETT/ \
    --data_path ETTh1.csv \
    --features M \
    --freq h \
    --seq_len 96 \
    --label_len 48 \
    --pred_len 96 \
    --enc_in 7 \
    --dec_in 7 \
    --c_out 7 \
    --d_model 512 \
    --n_heads 8 \
    --e_layers 2 \
    --d_layers 1 \
    --d_ff 2048 \
    --dropout 0.1 \
    --norm_type CAST-Norm

Supported Models

• Informer: Transformer-based model with ProbSparse attention
• S_Mamba: Mamba-based model with state space mechanisms
• DLinear: Linear model with series decomposition
• TCN: Temporal Convolutional Network

Dataset

Place your dataset CSV files in the ./data/ directory. The framework supports:

• ETT datasets (ETTh1, ETTh2, ETTm1, ETTm2)
• Custom datasets (use --data custom)

Key Parameters

• --norm_type: Normalization type (none or CAST-Norm)
• --cast_norm_denorm: Denormalization method (recalib, simple, or none)
• --enable_stcp: Enable Spatial-Temporal Coupling Perception module
• --enable_casd: Enable Community-Aware Spatial Purification module
• --lambda1: Weight for mincut and orthogonality losses
• --lambda2: Weight for consistency loss

Acknowledgement

We appreciate the following github repos a lot for their valuable code base or datasets:

https://github.com/thuml/Time-Series-Library

https://github.com/zhouhaoyi/Informer2020

https://github.com/wzhwzhwzh0921/S-D-Mamba

https://github.com/cure-lab/LTSF-Linear

https://github.com/luodhhh/ModernTCN