Online learning of Koopman operator using streaming data from different dynamical regimes
For researchers in data-driven modeling and control of complex systems, this method addresses the challenge of handling streaming data from multiple dynamical regimes, but the improvements are incremental over existing subspace identification and Koopman operator techniques.
The paper introduces an online learning framework for the Koopman operator that uses Grassmannian distance to detect novel dynamical regimes in streaming data, updating the model only when necessary. This approach reduces data usage and adaptively learns basis functions, optimizing model accuracy and system order.
The paper presents a framework for online learning of the Koopman operator using streaming data. Many complex systems for which data-driven modeling and control are sought provide streaming sensor data, the abundance of which can present computational challenges but cannot be ignored. Streaming data can intermittently sample dynamically different regimes or rare events which could be critical to model and control. Using ideas from subspace identification, we present a method where the Grassmannian distance between the subspace of an extended observability matrix and the streaming segment of data is used to assess the `novelty' of the data. If this distance is above a threshold, it is added to an archive and the Koopman operator is updated if not it is discarded. Therefore, our method identifies data from segments of trajectories of a dynamical system that are from different dynamical regimes, prioritizes minimizing the amount of data needed in updating the Koopman model and furthermore reduces the number of basis functions by learning them adaptively. Therefore, by dynamically adjusting the amount of data used and learning basis functions, our method optimizes the model's accuracy and the system order.