扩散过程自适应偏置势方法的收敛性分析
Convergence analysis of Adaptive Biasing Potential methods for diffusion processes
摘要：
本文讨论了一类应用于扩散过程的自适应重要抽样算法的数学分析。这些方法被称为自适应偏置电位方法，由于相关自由能函数的近似（相对于反应坐标），这些方法被设计为有效地对扩散过程的不变分布进行采样。在动态中引入的偏差是自适应计算的;它取决于通过一些时间平均值的过程的轨迹的过去。我们给出了这样的方法的详细和一般的建设。我们证明了该方法的一致性（几乎必然收敛的精心挑选的加权经验概率分布）。我们证明了效率由于一些定性和定量的额外参数。为了证明这些结果，我们重新审视和扩展工具，从随机逼近适用于自相互作用扩散，在原来的背景下。
英文摘要：
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently sample the invariant distribution of the diffusion process, thanks to the approximation of the associated free energy function (relative to a reaction coordinate). The bias which is introduced in the dynamics is computed adaptively; it depends on the past of the trajectory of the process through some time-averages. We give a detailed and general construction of such methods. We prove the consistency of the approach (almost sure convergence of well-chosen weighted empirical probability distribution). We justify the efficiency thanks to several qualitative and quantitative additional arguments. To prove these results , we revisit and extend tools from stochastic approximation applied to self-interacting diffusions, in an original context.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
