A kernel two-sample test is developed for deciding whether two dynamical systems are identical based on data streams from these systems. Such comparison of dynamical systems is relevant, for example, when evaluating model-based design, detecting anomalies in medical data, or for transferring knowledge from one system to another. Kernel two-sample tests are a well established statistical method for comparing probability distributions and have been applied to many diverse objects, yet rarely to dynamical systems. In this paper, we propose an extension of the kernel two-sample test to dynamical systems based on ergodicity theory. This measure-theoretical point of view on dynamical systems allows us to compare them in a meaningful way. In particular, we do not require synchronous sampling, identical initial conditions, or similar restrictive assumptions. We demonstrate the effectiveness of the proposed method experimentally on human walking data by detecting anomalies in walking patterns.
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