A Novel Hybrid Modeling Framework for Polymer Reaction Engineering with Application to Real-Time Process Monitoring

Hybrid modeling frameworks that integrate knowledge-driven and data-driven approaches offer a promising solution for modeling complex physical systems, especially when data are limited and domain knowledge is well established. In this work, a hybrid modeling strategy is proposed, coupling Gaussian Processes with a kinetic polymerization model for the case of the free-radical polymerization of styrene. The kinetic model serves as the mean function of the Gaussian Process prior embedding fundamental system knowledge into the regression process. The proposed framework enables the model to deliver physically consistent predictions in the absence of data while allowing fast adaptation when new data becomes available. This is demonstrated in a real-time process monitoring context, where data points arrive sequentially and the model updates its predictions accordingly, while avoiding the need for extensive training, typically required by DD models, such as neural networks. The approach is validated using two data sets across a wide range of reaction temperatures (85–150 °C), showcasing its performance under varying degrees of model-data agreement. The results highlight the framework’s ability to learn from limited data, maintain physical plausibility through constrained predictions, and incorporate uncertainty for improved robustness. This study, through a simple example, lays the groundwork for broader applications of Gaussian-Process-based hybrid models in polymerization systems, with future work aimed at extending their scope to additional process variables and constraint handling strategies.