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. To accelerate the deployment of transition detection algorithms in high-dimensional dynamical systems, we introduce dimensionality reduction techniques. Our experiments demonstrate that transitions can be detected efficiently, in real-time, for the two-dimensional forced Kolmogorov flow and the Rössler dynamical system, which are characterized by anomalous regimes in phase space where dynamics are perturbed off the attractor at potentially uneven intervals. Finally, we also demonstrate how variations in the frequency of detected changepoints may be utilized to detect a significant modification to the underlying model parameters by utilizing the Lorenz-63 dynamical system.
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October 2023
Research Article|
October 11 2023
Online data-driven changepoint detection for high-dimensional dynamical systems
Sen Lin
;
Sen Lin
a)
(Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing)
1
Department of Mathematics, University of Houston
, Houston, Texas 77004, USA
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Gianmarco Mengaldo
;
Gianmarco Mengaldo
(Formal analysis, Methodology, Writing – review & editing)
2
Department of Mechanical Engineering
, 9 Engineering Drive 1, 07-08 Block EA, Singapore
117575
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Romit Maulik
Romit Maulik
b)
(Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing)
3
Information Science and Technology and Institute for Computational and Data Sciences, Pennsylvania State University
, University Park, Pennsylvania 16802, USA
b)Author to whom correspondence should be addressed: [email protected]. Also at: Joint Appointment Faculty, Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA.
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b)Author to whom correspondence should be addressed: [email protected]. Also at: Joint Appointment Faculty, Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA.
a)
Work performed as Givens Associate at Argonne National Laboratory.
Citation
Sen Lin, Gianmarco Mengaldo, Romit Maulik; Online data-driven changepoint detection for high-dimensional dynamical systems. Chaos 1 October 2023; 33 (10): 103112. https://doi.org/10.1063/5.0160312
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