Accurate dynamic prediction of multi-effect distillation with thermal vapor compression (MED-TVC) systems is essential for online monitoring and control-oriented operation. However, these systems exhibit strong coupling and significant nonlinear dynamics, which significantly increase the difficulty of accurate forecasting. To address this, we propose a Nonstationary Spatial Attention Transformer (NSAT) for multivariate and multi-horizon forecasting. The NSAT employs feature-wise tokenization to preserve cross-variable dependencies and integrates an adaptive nonstationary correction module to mitigate distributional shifts, enhancing robustness under varying operating conditions. Furthermore, a spatial-attention encoder is introduced to capture multivariate process interactions in a physically interpretable and consistent manner. Evaluated on an industrial-scale water for injection unit dataset covering multiple steady-state and transient operating regimes, NSAT achieves superior predictive performance, with an average RMSE of 7.319, MAPE of 5.557%, and R 2 of 0.961, outperforming representative baseline models such as MLP, LSTM, Transformer, Informer, and N-BEATS. Even at extended forecasting horizons, the mean R 2 decreases by only about 9.5%. Furthermore, the learned attention patterns are consistent with the underlying physical process behavior, demonstrating the model's interpretability. Overall, NSAT provides a robust and interpretable framework for long-horizon dynamic prediction of MED-TVC systems and offers practical potential for control-oriented industrial deployment.
Feng et al. (2026) studied this question.