Neural Ordinary Differential Equation and Supervised Gated Recurrent Units Embedded with Historical Variables for Petrochemical Process Prediction

Gated recurrent units (GRU) effectively handle dynamic nonlinear data in petrochemical process. However, GRUs mainly focus on temporal dependencies of input variables while neglecting supervisory variables in historical data. Concurrently, conventional discrete-layer neural networks struggle to capture continuous-time system dynamics. These combined limitations impair long-term prediction accuracy. To overcome the limitations of existing time series modeling approaches in capturing complex dynamic behaviors, this study proposes a novel fusion framework that integrates a gated recurrent architecture with neural ordinary differential equations (Neural ODEs). Specifically, we introduce a supervised history-gated recurrent unit (SHGRU), which extends the standard GRU by incorporating historical supervisory variables, thereby enhancing the model’s capacity to capture time-varying hidden dynamics associated with process quality. Building on this foundation, a deep architecture SHGRU deep network (SHGRU-DN) is constructed by stacking multiple layers of SHGRU units, enabling hierarchical feature extraction guided by historical supervision. To further model the continuous-time evolution of system states, we embed an improved Neural ODE into the SHGRU-DN, resulting in a novel dynamic modeling framework termed SHGRU with dynamic Neural ODE (SHGRU-DODE). Extensive experiments on industrial datasets demonstrate the superior predictive accuracy of the proposed model compared to GRU, and the results are close to the true value with an RMSE of 0.0151 when predicting gasoline yield during fluid catalytic cracking. Additional evaluations on the tennessee eastman process and the debutanizer column further validate the model’s superiority.