Using machine learning to predict catastrophes in dynamical systems
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摘要
Nonlinear dynamical systems, which include models of the Earth’s climate, financial markets and complex ecosystems, often undergo abrupt transitions that lead to radically different behavior. The ability to predict such qualitative and potentially disruptive changes is an important problem with far-reaching implications. Even with robust mathematical models, predicting such critical transitions prior to their occurrence is extremely difficult. In this work, we propose a machine learning method to study the parameter space of a complex system, where the dynamics is coarsely characterized using topological invariants. We show that by using a nearest neighbor algorithm to sample the parameter space in a specific manner, we are able to predict with high accuracy the locations of critical transitions in parameter space.
论文关键词:65P99,37B30,68T05,37N99,Conley index,Dynamical systems,Machine learning
论文评审过程:Received 20 November 2010, Revised 1 September 2011, Available online 13 November 2011.
论文官网地址:https://doi.org/10.1016/j.cam.2011.11.006