StOKeDMD: Streaming Occupation kernel dynamic mode decomposition

Abstract

Dynamic mode decomposition (DMD) has become a common technique for constructing surrogate models for dynamical systems from observed system states. The Occupation Kernel DMD (OKDMD) method proposed in (Rosenfeld et al., 2022) and (Rosenfeld et al., 2024) is a Liouville operator based method that builds surrogate models from system state trajectories. Here, this paper proposes an extension of OKDMD to the case when the system states are observed in a streaming fashion, i.e., only a small fraction of the state trajectory is available at a given time. The developed method, Streaming Occupation Kernel DMD (StOKeDMD), accommodates the streaming data input by leveraging properties of specific choices of kernel functions and occupation kernels. We apply the StoKeDMD method as a compression method for streaming data, analyze the memory complexity, and demonstrate the performance of StoKeDMD in the compression of streaming data generated from a Lorenz system and a fluid flow simulation.