Crowd Flow Completion From Partial Spatial Observations Using Kernel DMD

In this paper, we address the problem of estimating the total flow of a crowd of pedestrians from spatially limited observations. Our approach relies on identifying a dynamical system regime that characterizes the observed flow in a limited spatial domain by solving for the modes and eigenvalues of the corresponding Koopman operator. We develop a framework where we first approximate the Koopman operator by computing the kernel dynamic mode decomposition (DMD) operator for different flow regimes using fully observed training data. We then pose flow completion as a least squares problem constrained by the one step evolution of the kernel DMD operator. We present numerical experiments with simulated pedestrian flows and demonstrate that the proposed approach succeeds in completing the flow from limited spatial observations.