Online data-driven changepoint detection for high-dimensional dynamical systems

Abstract

The detection of anomalies or transitions in complex dynamical systems is of critical importance to various applications. In this study, we propose the use of machine learning to detect changepoints for high-dimensional dynamical systems. Here, changepoints indicate instances in time when the underlying dynamical system has a fundamentally different characteristic - which may be due to a change in the model parameters or due to intermittent phenomena arising from the same model. We propose two complementary approaches to achieve this, with the first devised using arguments from probabilistic unsupervised learning and the latter devised using supervised deep learning. Our emphasis is also on detection for high-dimensional dynamical systems, for which we introduce the use of dimensionality reduction techniques to accelerate the deployment of transition detection algorithms. Our experiments demonstrate that transitions can be detected efficiently, in real-time, for the two-dimensional forced Kolmogorov flow, which is characterized by anomalous regimes in phase space where dynamics are perturbed off the attractor at uneven intervals.