📄 中文摘要
关键转变是系统在不同状态之间的突变，理解这些转变对于生态学、气候科学和生物学中的临界点至关重要。传统的检测方法通常需要大量的前向模拟或分岔分析，这些方法计算量大且受到参数采样的限制。研究提出了一种基于深度神经网络的新型机器学习方法，称为平衡信息神经网络（EINNs），用于识别与灾难性状态转变相关的临界阈值。EINN方法通过使用候选平衡状态反向处理，而不是固定参数并搜索解决方案，从而提高了检测效率和准确性。
复杂系统动态的机器学习：利用深度神经网络检测动态系统中的分岔
📄 English Summary
Machine Learning for Complex Systems Dynamics: Detecting Bifurcations in Dynamical Systems with Deep Neural Networks
Critical transitions represent abrupt shifts between qualitatively different states of a system, essential for understanding tipping points in complex dynamical systems across fields such as ecology, climate science, and biology. Traditional methods for detecting these shifts often rely on extensive forward simulations or bifurcation analyses, which can be computationally intensive and limited by parameter sampling. A novel machine learning approach is proposed, utilizing deep neural networks known as equilibrium-informed neural networks (EINNs) to identify critical thresholds associated with catastrophic regime shifts. The EINN method reverses the conventional process by leveraging candidate equilibrium states, enhancing detection efficiency and accuracy.