Incremental Learning Based Subspace Modeling for Distributed Parameter Systems

In this paper, a novel incremental learning based subspace modeling method is developed for spatiotemporal modeling of distributed parameter systems (DPSs). First, the streaming snapshots are collected into small batches at a preset time interval in an online mode. The initial batch belongs to the first nominal subspace. Second, the dissimilarity analysis is further utilized to assign each new batch to one of the existing subspaces or a new subspace. Third, the local basis functions corresponding to the assigned subspace is updated or generated through incremental learning of the new batch data. Finally, all the local models are ensembled to approximate the system’s dynamics over the whole time-space domain in real-time. The proposed method is tested on a hyperbolic advection system and a one-dimensional diffusion-reaction system. Results demonstrate that the proposed method is superior to the conventional global modeling, and achieves higher modeling accuracy for DPSs.