耦合振子中降维的自动发现
Automated discovery of dimensional reductions in coupled oscillators
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中文总结 AI 辅助
本文利用无监督自编码器自动发现耦合振子系统的低维宏观动力学，其内在维度与Watanabe-Strogatz理论一致，并在Kuramoto振子和约瑟夫森结中验证，同时证明无此特性的系统无显著降维。
中文摘要 AI 辅助
长期以来，人们一直在努力揭示由大量微观单元相互作用构成的系统中的低维宏观动力学，其中潜在的物理原理支配着这些系统向低维流形的坍缩。本文聚焦于相互作用的相位振子系统，证明了一种无监督自编码器框架能够确定其内在维度，这与Watanabe-Strogatz理论的预测一致。通过对潜在维度进行系统扫描，识别出解析预测的降维维度，而监督回归则证实了学习到的潜在变量捕获了理论Watanabe-Strogatz坐标中包含的全部信息。我们在两个原型系统中展示了这一能力：Kuramoto振子和电阻负载约瑟夫森结。我们进一步通过展示缺乏此类可约化动力学的系统不会表现出明显的维度缩减，确立了该框架的诊断特异性。
英文摘要
There have been persistent efforts to uncover low-dimensional macroscopic dynamics in large systems of interacting microscopic units, in which underlying physical principles govern their collapse onto low-dimensional manifolds. Here, focusing on interacting phase oscillator systems, we show that an unsupervised autoencoder framework can determine their intrinsic dimensionality, in agreement with the predictions of Watanabe-Strogatz theory. Systematic sweeps over the latent dimensions identify the analytically predicted reduced dimensions, while supervised regression confirms that the learned latent variables capture the full information contained in the theoretical Watanabe-Strogatz coordinates. We demonstrate this capability for two prototype systems: Kuramoto oscillators and resistively loaded Josephson junctions. We further establish the diagnostic specificity of the framework by showing that systems lacking such reducible dynamics do not exhibit a sharp dimensional reduction.
发表机构
- Indian Institute of Technology Indore（印度印多尔理工学院）
机构由 AI 辅助整理，请以论文原文为准。
