Active search for bifurcations.

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2025-05-01 DOI:10.1063/5.0226625
Yorgos M Psarellis, Themistoklis P Sapsis, Ioannis G Kevrekidis
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引用次数: 0

Abstract

Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding of observed dynamic behavior, but also for designing efficient interventions. When the dynamical system at hand is complex, possibly noisy, and expensive to sample, standard (e.g., continuation based) numerical methods may become impractical. We propose an active learning framework, where Bayesian Optimization is leveraged to discover saddle-node or Hopf bifurcations, from a judiciously chosen small number of vector field observations. Such an approach becomes especially attractive in systems whose state×parameter space exploration is resource-limited. It also naturally provides a framework for uncertainty quantification (aleatoric and epistemic), useful in systems with inherent stochasticity.

主动搜索分岔。
分岔标志着动力系统长期行为的质变,通常可以标志着突然(“硬”)转变或灾难性事件(分岔)。准确定位它们不仅对深入了解观察到的动态行为至关重要,而且对设计有效的干预措施也至关重要。当手头的动力系统很复杂,可能有噪声,采样成本高时,标准(例如,基于延拓的)数值方法可能变得不切实际。我们提出了一个主动学习框架,利用贝叶斯优化从明智选择的少量向量场观测中发现鞍节点或Hopf分岔。这种方法在state×parameter空间探索资源有限的系统中特别具有吸引力。它也自然地为不确定性量化(任意的和认知的)提供了一个框架,在具有固有随机性的系统中很有用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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