Online dynamic mode decomposition for time-varying systems

TL;DR

This paper introduces an efficient online dynamic mode decomposition (DMD) algorithm that updates system models in real time without storing past data, suitable for analyzing time-varying systems and capable of handling large datasets.

Contribution

The work presents a novel real-time DMD algorithm using rank-1 updates, incorporating data weighting and windowed analysis, outperforming existing methods in efficiency for low to moderate state dimensions.

Findings

Most efficient for state dimensions less than 200

Orders of magnitude faster than standard DMD

Effectively captures dynamics in complex flow data

Abstract

Dynamic mode decomposition (DMD) is a popular technique for modal decomposition, flow analysis, and reduced-order modeling. In situations where a system is time varying, one would like to update the system's description online as time evolves. This work provides an efficient method for computing DMD in real time, updating the approximation of a system's dynamics as new data becomes available. The algorithm does not require storage of past data, and computes the exact DMD matrix using rank-1 updates. A weighting factor that places less weight on older data can be incorporated in a straightforward manner, making the method particularly well suited to time-varying systems. A variant of the method may also be applied to online computation of "windowed DMD", in which only the most recent data are used. The efficiency of the method is compared against several existing DMD algorithms: for problems in which the state dimension is less than about~200, the proposed algorithm is the most efficient for real-time computation, and it can be orders of magnitude more efficient than the standard DMD algorithm. The method is demonstrated on several examples, including a time-varying linear system and a more complex example using data from a wind tunnel experiment. In particular, we show that the method is effective at capturing the dynamics of surface pressure measurements in the flow over a flat plate with an unsteady separation bubble.