论文标题
通过非感知阴影算法近似线性响应
Approximating linear response by nonintrusive shadowing algorithms
论文作者
论文摘要
非引人入胜的阴影算法有效地计算$ v $，阴影轨迹之间的差异，然后使用$ v $计算混乱目标的平均目标衍生物，相对于动态系统的参数。但是，先前的阴影方法证明错误地假设阴影轨迹是代表性的。相反，线性响应公式被严格证明，但更难计算。 我们证明，$ v $仅给出了线性响应的一部分，称为阴影贡献；因此，另一部分是不稳定的贡献，是阴影方法的系统误差。对于不稳定维度比例较小的系统，并具有进一步的统计假设，我们表明不稳定的贡献很小。我们还简要描述了一种不稳定贡献的算法，该算法比快速线性响应算法更简单但效率较低。 此外，我们证明了非感染阴影算法（最快的阴影算法）与$ v $的融合以及阴影的贡献。
Nonintrusive shadowing algorithms efficiently compute $v$, the difference between shadowing trajectories, then use $v$ to compute derivatives of averaged objectives of chaos with respect to parameters of the dynamical system. However, previous proofs of shadowing methods wrongly assume that shadowing trajectories are representative. In contrast, the linear response formula is proved rigorously, but is more difficult to compute. We prove that $v$ gives only a part, called the shadowing contribution, of the linear response; hence, the other part, the unstable contribution, is the systematic error of shadowing methods. For systems with a small ratio of unstable dimensions, with some further statistical assumptions, we show that the unstable contribution is small. We also briefly describe an algorithm for the unstable contribution, which is simpler to derive but less efficient than the fast linear response algorithm. Moreover, we prove the convergence of the nonintrusive shadowing algorithm, the fastest shadowing algorithm, to $v$ and to the shadowing contribution.
