Predicting high-codimension critical transitions in dynamical systems using active learning |
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Authors: | Kelly Spendlove Jesse Berwald Tomáš Gedeon |
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Institution: | 1. Department of Mathematical Sciences, Montana State University, Bozeman, MT 59718, USAspendlove@math.montana.edu;3. Department of Mathematics, The College of William and Mary, Williamsburg, VA 23185, USA;4. Department of Mathematical Sciences, Montana State University, Bozeman, MT 59718, USA |
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Abstract: | Complex dynamical systems, from those appearing in physiology and ecology to Earth system modelling, often experience critical transitions in their behaviour due to potentially minute changes in their parameters. While the focus of much recent work, predicting such bifurcations is still notoriously difficult. We propose an active learning approach to the classification of parameter space of dynamical systems for which the codimension of bifurcations is high. Using elementary notions regarding the dynamics, in combination with the nearest-neighbour algorithm and Conley index theory to classify the dynamics at a predefined scale, we are able to predict with high accuracy the boundaries between regions in parameter space that produce critical transitions. |
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Keywords: | dynamical systems Conley index machine learning combinatorial dynamics |
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