SSVT: Industrial Multivariate Time Series Forecasting with Hybrid State Space and Variate-Token Attention

As industrial systems operate at higher sampling rates and deploy increasingly dense sensor networks, multivariate time series forecasting in industrial settings faces two central challenges, namely slow cross-cycle drift that accumulates over long temporal spans and abrupt local fluctuations across variables. To address these challenges, we propose SSVT, a new paradigm for industrial multivariate time series forecasting that integrates hybrid state-space modeling with variate-token attention. Specifically, a temporal state-space encoder extracts cross-cycle historical dynamics for each variable and maps the resulting state representation into a corresponding variate token, allowing the tokens to retain long-term drift information along the temporal dimension. Variate-token attention then propagates information across variables and models local inter-variable dependencies, enabling SSVT to jointly capture long-term trends and short-term fluctuations. Building on this architecture, we further introduce physical constraints into the training process and use an LLM to assist in configuring the constraint weights. This design provides a more effective balance between data-driven learning and physical priors, improving forecasting stability and generalization in complex industrial environments. Experiments on six datasets show that the advantage of SSVT becomes increasingly pronounced as the forecasting horizon extends. In the 720-step forecasting task, SSVT achieves the best MSE and MAE across all six datasets. On the Boiler Equipment dataset, SSVT obtains an average MSE of 0.395, reducing the error by 6.95% compared with the strongest baseline. These results indicate that SSVT offers an effective paradigm for modeling cross-cycle slow drift and local variable dependencies in industrial time series. The code and experimental configurations will be made publicly available at https://github.com/CollaborativeResearch/SSVT.