A dynamic PCA and transformers coupled reduced-order model for transient solid-liquid flows in stirred tanks

Solid-liquid mixing in stirred tanks is critical in industries such as pharmaceuticals and chemicals, where uniform mixing enhances product quality and operational efficiency. In this study, a reduced-order model (ROM) based on dynamic Principal Component Analysis (DPCA) and Transformer coupled approach was developed to predict transient solid-liquid mixing dynamics in stirred tanks. The model leverages DPCA to decompose the system’s spatial dynamics and captures the temporal evolution with a Transformer network. The results showed that DPCA significantly reduced the dimensionality of the system, while the Transformer model captured the temporal dynamics effectively. The DPCA decomposition revealed flow structures with cylindrical symmetry, particularly around the impellers, which are crucial for understanding mixing efficiency. This work demonstrates the feasibility of combining DPCA and Transformer networks for real-time, and optimization of industrial mixing processes, offering a significant reduction in computational costs while maintaining predictive accuracy.