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Most existing digital twins rely on data-driven black-box models,predominantly using deep neural recurrent, and convolutional neural networks(DNNs, RNNs, and CNNs) to capture the dynamics of chemical systems. However,these models have not seen the light of day, given the hesitance of directlydeploying a black-box tool in practice due to safety and operational issues. Totackle this conundrum, hybrid models combining first-principles physics-baseddynamics with machine learning (ML) models have increased in popularity as theyare considered a 'best of both worlds' approach. That said, existing simple DNNmodels are not adept at long-term time-series predictions and utilizingcontextual information on the trajectory of the process dynamics. Recently,attention-based time-series transformers (TSTs) that leverage multi-headedattention mechanism and positional encoding to capture long-term and short-termchanges in process states have shown high predictive performance. Thus, afirst-of-a-kind, TST-based hybrid framework has been developed for batchcrystallization, demonstrating improved accuracy and interpretability comparedto traditional black-box models. Specifically, two different configurations(i.e., series and parallel) of TST-based hybrid models are constructed andcompared, which show a normalized-mean-square-error (NMSE) in the range of$[10, 50]\times10^{-4}$ and an $R^2$ value over 0.99. Given the growingadoption of digital twins, next-generation attention-based hybrid models areexpected to play a crucial role in shaping the future of chemicalmanufacturing.

Introducing Hybrid Modeling with Time-series-Transformers: A Comparative Study of Series and Parallel Approach in Batch Crystallization