Connection between nonlinear energy optimization and instantons.
Connection between nonlinear energy optimization and instantons.
复制标题
DOI：
10.1103/physreve.97.012212
复制
发表时间：
2018-04
期刊：
影响因子：
--
通讯作者：
D. Lecoanet;R. Kerswell
中科院分区：
文献类型：
--
作者：
D. Lecoanet;R. Kerswell
在外界扰动下，系统如何在不同的稳定状态之间转换是一个重要的实际问题。我们讨论了最近发展起来的一种能量最优化方法，用于识别到达稳定状态盆地边界所需的最小扰动，该方法如何与噪声系统大偏差理论中的瞬子轨迹相联系。在具有多个稳定平衡点的一维Swift-Hohenberg方程的背景下，我们首先展示了如何直接使用能量优化方法来识别从基态过渡到特定吸引子的最小扰动-最小种子。然后，在将该方法推广到考虑多个等间隔时间扰动后，证明了瞬子轨迹确实是能量最优化方法在无限多个扰动极限下的解，只要用特定的范数来度量离散扰动集。重要的是，我们发现瞬子的关键特征可以通过少量的离散微扰来捕捉(通常情况下，每穿过一个吸引盆就有一个微扰)。这为计算瞬子可能不切实际的系统提供了一种很有前途的新诊断方法。
How systems transit between different stable states under external perturbation is an important practical issue. We discuss here how a recently developed energy optimization method for identifying the minimal disturbance necessary to reach the basin boundary of a stable state is connected to the instanton trajectory from large deviation theory of noisy systems. In the context of the one-dimensional Swift-Hohenberg equation, which has multiple stable equilibria, we first show how the energy optimization method can be straightforwardly used to identify minimal disturbances-minimal seeds-for transition to specific attractors from the ground state. Then, after generalizing the technique to consider multiple, equally spaced-in-time perturbations, it is shown that the instanton trajectory is indeed the solution of the energy optimization method in the limit of infinitely many perturbations provided a specific norm is used to measure the set of discrete perturbations. Importantly, we find that the key features of the instanton can be captured by a low number of discrete perturbations (typically one perturbation per basin of attraction crossed). This suggests a promising new diagnostic for systems for which it may be impractical to calculate the instanton.