论文标题
用于区分混乱的快速线性响应算法
Fast linear response algorithm for differentiating chaos
论文作者
论文摘要
我们设计了快速线性响应算法，以区分混乱的分形不变量相对于管理方程的扰动。我们首先得出了不稳定差异的第一个可计算扩展公式，然后通过重新归一化的二阶切线方程来得出一个“快速”公式。该算法的成本仅求解一个轨道和$ u $，不稳定的尺寸，许多一阶和二阶切线方程；主要错误是轨道的采样误差。我们在一个数值示例上进行了证明，这对于以前的方法很难。
We devise the fast linear response algorithm for differentiating fractal invariant measures of chaos with respect to perturbations of governing equations. We first derive the first computable expansion formula for the unstable divergence, then a `fast' formula by renormalized second-order tangent equations. The algorithm's cost is solving only one orbit and $u$, the unstable dimension, many first-order and second-order tangent equations; the main error is the sampling error of the orbit. We demonstrate it on an numerical example which is difficult for previous methods.
