Multi-trajectory Dynamic Mode Decomposition

Abstract

We propose a new interpretation of the parameter optimization in dynamic mode decomposition (DMD), and show a rigorous application in multi-trajectory modeling. The proposed method, multi-trajectory DMD (MTDMD) is a numerical method using which we can model a dynamical system using multiple trajectories, or multiple sets of consecutive snapshots. Here, a trajectory corresponds to an experiment, so the proposed method accepts multiple experimental results. This is in a clear contrast to the existing DMD-based methods that accept only one set of consecutive snapshots.
Abovementioned multi-trajectory modeling is quite useful in applications, because we can suppress the undesirable effects from the observation noises and employ multiple experiments with different
experimental conditions to model a complex system.
The proposed method is quite flexible, and we suggest that we can also implement L2 regularization and element-wise equality constraints on the model parameters. We expect that the proposed method is useful to model large complex systems in the industrial applications.