Online dynamic mode decomposition for time-varying systems
For researchers in fluid dynamics and reduced-order modeling, this provides a computationally efficient way to track time-varying systems in real time, though the improvement is incremental over existing DMD variants.
This work introduces an efficient online algorithm for dynamic mode decomposition (DMD) that updates the system's dynamics in real time using rank-1 updates without storing past data, achieving orders of magnitude speedup over standard DMD for state dimensions under ~200. The method is demonstrated on time-varying systems and wind tunnel data, effectively capturing unsteady flow dynamics.
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.