用神经网络从振荡数据中识别相空间的隐含几何结构。
Machine learning identifies nullclines in oscillatory dynamical systems
- 基于神经网络学习振荡系统的相空间静态度量特征。
- 在多时间尺度与强非线性下仍能准确识别零曲面。
- 结果可转为符号微分方程，适合动力系统研究者使用。
我们提出CLINE（Computational Learning and Identification of Nullclines），一种基于神经网络的方法，可从振荡时间序列数据中揭示系统隐含的零曲面结构。与直接预测系统动态的传统方法不同，CLINE聚焦于相空间中编码状态变量间（非）线性关系的静态几何特征。该方法克服了多时间尺度和强非线性带来的挑战，同时生成可解释的结果，并可转化为符号微分方程。我们在多种振荡系统上验证了CLINE的有效性。
原文摘要 · Abstract (English)
We introduce CLINE (Computational Learning and Identification of Nullclines), a neural network-based method that uncovers the hidden structure of nullclines from oscillatory time series data. Unlike traditional approaches aiming at direct prediction of system dynamics, CLINE identifies static geometric features of the phase space that encode the (non)linear relationships between state variables. It overcomes challenges such as multiple time scales and strong nonlinearities while producing interpretable results convertible into symbolic differential equations. We validate CLINE on various oscillatory systems, showcasing its effectiveness.
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