Efficient incremental model reduction approach for time-varying spatially distributed processes

The accurate and efficient modeling of complex spatially distributed processes (SDPs) represents a significant challenge for researchers in the field. A variety of modeling approaches have been developed with the objective of addressing issues related to spatiotemporal modeling. The conventional offline modeling approaches necessitate the availability of a spatiotemporal data set that encompasses the entirety of the system’s dynamic features. It is not possible to fully satisfy this prerequisite in the context of real-world applications, particularly in the case of time-varying SDPs. Furthermore, the process of updating the model by repeatedly applying the offline algorithm is inherently time-consuming. In this paper, we put forth an efficient incremental model reduction approach for time-varying SDPs. Following the initialization phase, the modified Gram–Schmidt orthogonalization method is employed to extract the feature subspace in a sequential manner. The time-space synthesis is then utilized to reconstruct the spatiotemporal dynamics. The efficacy of the model is evaluated on a representative diffusion-reaction process, and the comparative experimental outcomes demonstrate that the presented algorithm is an efficient and effective approach for the online learning of time-varying SDPs.