Evangelou Nikolaos, Cui Tianqi, Bello-Rivas Juan M, Makeev Alexei, Kevrekidis Ioannis G
Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA.
Faculty of Computational Mathematics and Cybernetics, Moscow State University, 119991 Moscow, Russia.
Chaos. 2024 Jun 1;34(6). doi: 10.1063/5.0187511.
We study the tipping point collective dynamics of an adaptive susceptible-infected-susceptible (SIS) epidemiological network in a data-driven, machine learning-assisted manner. We identify a parameter-dependent effective stochastic differential equation (eSDE) in terms of physically meaningful coarse mean-field variables through a deep-learning ResNet architecture inspired by numerical stochastic integrators. We construct an approximate effective bifurcation diagram based on the identified drift term of the eSDE and contrast it with the mean-field SIS model bifurcation diagram. We observe a subcritical Hopf bifurcation in the evolving network's effective SIS dynamics that causes the tipping point behavior; this takes the form of large amplitude collective oscillations that spontaneously-yet rarely-arise from the neighborhood of a (noisy) stationary state. We study the statistics of these rare events both through repeated brute force simulations and by using established mathematical/computational tools exploiting the right-hand side of the identified SDE. We demonstrate that such a collective SDE can also be identified (and the rare event computations also performed) in terms of data-driven coarse observables, obtained here via manifold learning techniques, in particular, Diffusion Maps. The workflow of our study is straightforwardly applicable to other complex dynamic problems exhibiting tipping point dynamics.
我们以数据驱动、机器学习辅助的方式研究自适应易感-感染-易感（SIS）流行病网络的临界点集体动力学。通过受数值随机积分器启发的深度学习ResNet架构，我们根据物理意义明确的粗粒度平均场变量确定了一个参数依赖的有效随机微分方程（eSDE）。我们基于所确定的eSDE的漂移项构建了一个近似有效的分岔图，并将其与平均场SIS模型分岔图进行对比。我们观察到在演化网络的有效SIS动力学中存在一个亚临界霍普夫分岔，它导致了临界点行为；这种行为表现为大振幅集体振荡，这种振荡自发但很少地从（有噪声的）稳态邻域中出现。我们通过重复的强力模拟以及使用利用所确定的SDE右侧的既定数学/计算工具来研究这些罕见事件的统计特性。我们证明，通过流形学习技术（特别是扩散映射）在此处获得的数据驱动粗粒度可观测量，也能够确定这样一个集体SDE（并且也能够执行罕见事件计算）。我们研究的工作流程可直接应用于表现出临界点动力学的其他复杂动态问题。
