Adaptive dual-domain fusion for online time series forecasting with offline knowledge

Accurate time series forecasting enables significant time savings and economic loss reduction. Although various advanced forecasting models have been developed, several challenges remain: (1) Most current models operate under offline settings, exhibiting limited capability for real-time processing of streaming data; (2) Existing online forecasting approaches either exclusively capture intra-variable dependencies or inter-variable interactions, with few studies achieving effective dynamic integration of both aspects, while also failing to leverage the benefits of prior offline knowledge. Therefore, we propose an online adaptive dual-domain fusion network with offline knowledge (OnADFNet) for online forecasting. First, we employ an online learning layer with memory capability to achieve online learning, which effectively handles evolving concept drift patterns. To comprehensively capture the nonlinear complexity of time series, we integrate offline multilayer perceptrons with the online learning layer to model intra-variable dependencies. For inter-variable correlations, we incorporate a multi-head attention mechanism on top of the online learning layer. Unlike Transformer-based approaches for time series, we first reverse the embedding representation of time series before processing, enabling more accurate and realistic extraction of cross-variable interactions. Finally, we dynamically adjust the long- and short-term weights of the two components using exponential gradient descent and offline reinforcement learning for integration, achieving adaptive online learning for the model. Experimental results show that our model reduces the mean squared error (MSE) by an average of 19.6 % compared to state-of-the-art methods and achieves a 26 % reduction in MSE in long-term predictions.