Real-time update of data-driven reduced and full order models with applications

We consider a dynamic mode decomposition (DMD) based technique to identify data-driven reduced-order and full-order models and propose two approaches to update them in real-time. These updates are crucial for the models to adapt to the evolving process. The proposed approaches function by calculating the update of the singular value decomposition (SVD), which is the core operation in DMD. In particular, two approaches involving temporal updates and additive modifications are used to update the SVDs. Further, the equivalence of both approaches is proved under special rank conditions. Also, the computational costs involved in these approaches are discussed. The technique is well suited for adaptive process modeling that can be exploited for real-time process monitoring, estimation, control, and optimization. The efficacy of the proposed approach is demonstrated using a large-scale benchmark wastewater treatment process.