自适应多层分裂在高维动力系统中的应用
Application of Adaptive Multilevel Splitting to High-Dimensional Dynamical Systems
摘要：
随机非线性动力系统可以经历相对于其强迫的变化的快速转变，例如由于在特定参数区间内出现多个平衡解。在本文中，我们修改的方法之一，计算概率的这种过渡，轨迹自适应多级采样（TAMS），能够将其应用到高维系统。关键的创新是一个预计的时间步进的方法，这导致了计算成本，特别是内存使用的大幅减少。通过大西洋环流崩溃的一个例子，这种新的实施TAMS的性能进行了研究。
英文摘要：
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we modify one of the methods developed to compute probabilities of such transitions, Trajectory-Adaptive Multilevel Sampling (TAMS), to be able to apply it to high-dimensional systems. The key innovation is a projected time-stepping approach, which leads to a strong reduction in computational costs, in particular memory usage. The performance of this new implementation of TAMS is studied through an example of the collapse of the Atlantic Ocean Circulation.
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