An algorithm is developed for determining the potential barrier height experimentally, provided that we have control over the noise strength $$\sigma $$ σ . We are concerned with the situation when the laboratory or numerical experiment requires large resources of time or computational power, respectively, and wish to find a protocol that provides the best estimate in a given amount of time. The optimal noise strength $$\sigma ^*$$ σ ∗ to use is found to be very simply related to the potential barrier height $$\Delta \Phi $$ Δ Φ as: $$y^*=\Delta \Phi ^{-1}$$ y ∗ = Δ Φ - 1 , $$y=\sigma ^{-2}-\sigma ^{-2}_\mathrm{a}$$ y = σ - 2 - σ a - 2 , with some “anchor point” $$\sigma ^{-2}_\mathrm{a}$$ σ a - 2 ; and, as a second ingredient, an iterative method is proposed for the estimation. For a numerical verification of the optimality , we apply the algorithm to a simple system of an over-damped particle confined to a double-well potential, when it is feasible to evaluate statistics of the estimator. Subsequently, we also apply it to a high-dimensional case of a diffusive energy balance model, when the potential barrier height—concerning e.g. the warm-to-snowball-climate transition—cannot be determined analytically, but we would have to resort to more sophisticated numerical methods.

中文翻译：

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从噪声引起的逃逸时间数据估计潜在障碍高度的有效算法

如果我们可以控制噪声强度 $$\sigma $$ σ ，则开发了一种用于通过实验确定势垒高度的算法。我们关注实验室或数值实验分别需要大量时间资源或计算能力的情况，并希望找到在给定时间内提供最佳估计的协议。发现要使用的最佳噪声强度 $$\sigma ^*$$ σ ∗ 与势垒高度 $$\Delta \Phi $$ Δ Φ 非常简单相关： $$y^*=\Delta \Phi ^{-1}$$ y ∗ = Δ Φ - 1 , $$y=\sigma ^{-2}-\sigma ^{-2}_\mathrm{a}$$ y = σ - 2 - σ a - 2 ，带有一些“锚点” $$\sigma ^{-2}_\mathrm{a}$$ σ a - 2 ; 并且，作为第二个要素，提出了一种用于估计的迭代方法。对于最优性的数值验证，当评估估计器的统计数据可行时，我们将该算法应用于受限于双阱势的过阻尼粒子的简单系统。随后，我们还将其应用于扩散能量平衡模型的高维情况，当势垒高度（例如关于暖到雪球气候转变）无法通过分析确定，但我们将不得不求助于更多复杂的数值方法。