用深度学习预测离散时间分岔
Predicting discrete-time bifurcations with deep learning
AI总结：
本文训练深度学习分类器为五个余维一离散时间分岔提供早期预警信号，在模拟及实验数据上优于常用方法，尤其对倍周期、Neimark-Sacker和折叠分岔预测准确率高。
摘要：
许多自然和人工系统都容易发生临界转变——即动力学中突然且可能具有破坏性的变化。深度学习分类器可以通过从大规模模拟训练数据集中学习分岔（动力学不稳定性）的通用特征，为临界转变提供早期预警信号（EWS）。迄今为止，分类器仅被训练用于预测连续时间分岔，忽略了离散时间分岔所特有的丰富动力学。在此，我们训练了一个深度学习分类器，为余维1的五个局部离散时间分岔提供早期预警信号。我们在来自生理学、经济学和生态学中离散时间模型的模拟数据，以及经历倍周期分岔的自发搏动鸡胚心肌聚集体的实验数据上测试了该分类器。在广泛的噪声强度和接近分岔速率的条件下，该分类器优于常用的早期预警信号。它还在大多数情况下预测了正确的分岔类型，其中对倍周期、Neimark-Sacker和折叠分岔的准确率特别高。深度学习作为分岔预测的工具仍处于萌芽阶段，并有可能改变我们监测系统临界转变的方式。
英文摘要：
Many natural and man-made systems are prone to critical transitions -- abrupt and potentially devastating changes in dynamics. Deep learning classifiers can provide an early warning signal (EWS) for critical transitions by learning generic features of bifurcations (dynamical instabilities) from large simulated training data sets. So far, classifiers have only been trained to predict continuous-time bifurcations, ignoring rich dynamics unique to discrete-time bifurcations. Here, we train a deep learning classifier to provide an EWS for the five local discrete-time bifurcations of codimension-1. We test the classifier on simulation data from discrete-time models used in physiology, economics and ecology, as well as experimental data of spontaneously beating chick-heart aggregates that undergo a period-doubling bifurcation. The classifier outperforms commonly used EWS under a wide range of noise intensities and rates of approach to the bifurcation. It also predicts the correct bifurcation in most cases, with particularly high accuracy for the period-doubling, Neimark-Sacker and fold bifurcations. Deep learning as a tool for bifurcation prediction is still in its nascence and has the potential to transform the way we monitor systems for critical transitions.
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。
