Anomaly detection in dynamical systems from measured time series

The paper addresses a problem of abnormalities detection in nonlinear processes represented by measured time series. Anomaly detection problem is usually formulated as finding outlier data points relative to some usual signals such as unexpected spikes, drops, or trend changes. In nonlinear dynamical systems, there are cases where a time series does not contain statistical outliers while the process corresponds to an abnormal configuration of the dynamical system. Since the polynomial neural architecture has a strong connection with the theory of differential equations, we use it for the feature extraction that describes the dynamical system itself. The paper discusses in both simulations and a practical example with real measurements the applicability of the proposed approach and it's benchmarking with existing methods.