OTformer: Non-Stationarity-Aware Adaptive Optimal Transport Attention for Time Series Forecasting

Time series forecasting is important in applications such as energy management, climate modeling, traffic control, and industrial monitoring. Recent variate-tokenization Transformers model cross-variate dependencies effectively, but Softmax attention still suffers from uneven cross-variate routing and fixed attention sharpness under varying non-stationarity. To address these limitations, OTformer is introduced as a non-stationarity-aware Optimal Transport framework for time series forecasting. A lightweight scorer estimates sample-wise non-stationarity from raw pre-normalization statistics and uses this signal to adapt the Sinkhorn entropy regularization coefficient ε, yielding smoother transport plans for more non-stationary inputs and sharper routing for more stationary ones. A shared phase embedding further injects cycle-aware context into variate tokens. Experiments on eight standard benchmarks and 32 forecasting settings show that OTformer consistently improves upon the iTransformer backbone, with average MSE reductions of 4.4% on ECL and 12.5% on Solar across four forecasting horizons.