复杂系统动力学中的机器学习：利用深度神经网络检测动力系统中的分岔现象
Machine Learning for Complex Systems Dynamics: Detecting Bifurcations in Dynamical Systems with Deep Neural Networks
AI总结：
本文提出基于深度神经网络的EINNs方法，用于检测复杂系统中临界转变的阈值，通过平衡状态输入推断参数以识别灾难性制度转变。
摘要：
临界转变是系统从一种定性不同的状态突然转变的过程，对于理解生态、气候科学和生物学中复杂动力系统中的临界点至关重要。检测这些转变通常涉及大量的正向模拟或分岔分析，这些方法往往计算成本高且受参数采样限制。在本研究中，我们提出了一种基于深度神经网络（DNNs）的新机器学习方法，称为平衡感知神经网络（EINNs），用于识别与灾难性制度转变相关的临界阈值。与其固定参数并寻找解不同，EINN方法通过将候选平衡状态作为输入，并训练DNN来推断满足平衡条件的相应系统参数。通过分析学习到的参数景观并观察平衡映射的可行性或连续性中的突变，可以有效检测临界阈值。我们在具有鞍点-节点分岔和多稳态的非线性系统上展示了这种方法的能力，证明EINNs可以恢复与即将发生的转变相关的参数区域。该方法为传统技术提供了一种灵活的替代方案，为高维和非线性系统中临界转变的早期检测和结构提供了新的见解。
英文摘要：
Critical transitions are the abrupt shifts between qualitatively different states of a system, and they are crucial to understanding tipping points in complex dynamical systems across ecology, climate science, and biology. Detecting these shifts typically involves extensive forward simulations or bifurcation analyses, which are often computationally intensive and limited by parameter sampling. In this study, we propose a novel machine learning approach based on deep neural networks (DNNs) called equilibrium-informed neural networks (EINNs) to identify critical thresholds associated with catastrophic regime shifts. Rather than fixing parameters and searching for solutions, the EINN method reverses this process by using candidate equilibrium states as inputs and training a DNN to infer the corresponding system parameters that satisfy the equilibrium condition. By analyzing the learned parameter landscape and observing abrupt changes in the feasibility or continuity of equilibrium mappings, critical thresholds can be effectively detected. We demonstrate this capability on nonlinear systems exhibiting saddle-node bifurcations and multi-stability, showing that EINNs can recover the parameter regions associated with impending transitions. This method provides a flexible alternative to traditional techniques, offering new insights into the early detection and structure of critical shifts in high-dimensional and nonlinear systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
