论文标题
数据驱动的粗粒度异构网络动力学的管理方程发现
Data-driven discovery of governing equations for coarse-grained heterogeneous network dynamics
论文作者
论文摘要
我们利用数据驱动的模型发现方法来确定异构网络动力学系统紧急行为的管理方程。具体而言，我们考虑了耦合的非线性振荡器的网络，其集体行为接近极限周期。稳定的极限循环在许多生物学应用中引起了人们的关注，因为它们对自维持的振荡进行了建模（例如心跳，化学振荡，神经元射击，昼夜节律）。对于显示松弛振荡的系统，我们的方法会自动检测动态中的边界（时间）层结构，拟合内部和外部解决方案，并以数据驱动的方式匹配它们。我们演示了有关良好系统的方法：瑞利振荡器和范德波尔振荡器。然后，我们将数学框架应用于在半同步的Kuramoto，Rayleigh，Rossler和Fitzhugh-Nagumo振荡器以及其异质组合的网络中发现低维动力学。我们还提供了集体网络动力学的维度作为几个网络参数的函数的数值探索，表明可以通过建议的体系结构来发现粗粒变量和动态。
We leverage data-driven model discovery methods to determine the governing equations for the emergent behavior of heterogeneous networked dynamical systems. Specifically, we consider networks of coupled nonlinear oscillators whose collective behaviour approaches a limit cycle. Stable limit-cycles are of interest in many biological applications as they model self-sustained oscillations (e.g. heart beats, chemical oscillations, neurons firing, circadian rhythm). For systems that display relaxation oscillations, our method automatically detects boundary (time) layer structures in the dynamics, fitting inner and outer solutions and matching them in a data-driven manner. We demonstrate the method on well-studied systems: the Rayleigh Oscillator and the Van der Pol Oscillator. We then apply the mathematical framework to discovering low-dimensional dynamics in networks of semi-synchronized Kuramoto, Rayleigh, Rossler, and Fitzhugh-Nagumo oscillators, as well as heterogeneous combinations thereof. We also provide a numerical exploration of the dimension of collective network dynamics as a function of several network parameters, showing that the discovery of coarse-grained variables and dynamics can be accomplished with the proposed architecture.
