论文标题
关于定期驱动系统正常双曲线不变流形动力学的神经网络方法
Neural network approach for the dynamics on the normally hyperbolic invariant manifold of periodically driven systems
论文作者
论文摘要
多维系统中的化学反应通常由等级-1鞍形描述，该鞍形鞍形在正常双曲线不变的歧管（NHHIM）中相交的稳定和不稳定的歧管相交。原则上，轨迹始于NHIM，当及时传播时，切勿离开这种流形。但是，由于运动的不稳定，对NHIM动力学的数值研究很困难。我们应用神经网络来描述时间依赖性的NHIM，并使用该网络稳定NHIM上的运动，以定期驱动的模型系统具有两个自由度。该方法使我们能够通过poincaré表面（PSO）分析NHIM上的动力学，并确定过渡态（TS）轨迹作为与驾驶鞍座相同周期性的周期轨道，即。 PSO的固定点被近乎综合的托里包围。基于过渡状态理论和对周期性TS轨迹的FLOQUET分析，与大型轨迹集合的传播相比，我们计算了反应的速率常数，并大大减少了数值努力。
Chemical reactions in multidimensional systems are often described by a rank-1 saddle, whose stable and unstable manifolds intersect in the normally hyperbolic invariant manifold (NHIM). Trajectories started on the NHIM in principle never leave this manifold when propagated forward or backward in time. However, the numerical investigation of the dynamics on the NHIM is difficult because of the instability of the motion. We apply a neural network to describe time-dependent NHIMs and use this network to stabilize the motion on the NHIM for a periodically driven model system with two degrees of freedom. The method allows us to analyze the dynamics on the NHIM via Poincaré surfaces of section (PSOS) and to determine the transition state (TS) trajectory as a periodic orbit with the same periodicity as the driving saddle, viz. a fixed point of the PSOS surrounded by near-integrable tori. Based on Transition State Theory and a Floquet analysis of a periodic TS trajectory we compute the rate constant of the reaction with significantly reduced numerical effort compared to the propagation of a large trajectory ensemble.
