采样局部自由能极小值的一种双尺度方法
A two-scale approach for sampling local free energy minimisers
- Mines de Saint-Etienne（圣艾蒂安国立高等矿业学院）
- LAMA, Université Gustave Eiffel（拉玛，巴黎-塞纳大学）
- Institut Universitaire de France（法兰西学术院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种双尺度方法，通过耦合慢宏观变量与粒子系统，使经验分布采样自由能的所有局部极小值，且转变时间与粒子数无关，受对数索博列夫不等式证明工具启发。
AI中文摘要：
当自由能具有多个局部极小值时，相应的平均场粒子系统表现出亚稳态行为，在这些极小值之间发生随机转变。然而，当粒子数量很大时，这些转变是罕见事件，通常发生在模拟无法企及的时间尺度上。在这项工作中，我们引入了一个与缓慢的宏观外部变量耦合的粒子系统，该变量近似遵循与粗粒化自由能相关的朗之万动力学。因此，粒子系统的经验分布对所有初始自由能的局部极小值进行采样，其转变时间现在与粒子数量无关。该构造受到一个理论工具的启发：用于证明吉布斯测度的对数索博列夫不等式的双尺度方法。
英文摘要：
When a free energy admits several local minimisers, the associated mean-field particle system exhibits a metastable behavior, undergoing random transitions between these minimisers. However, when the number of particles is large, these transitions are rare events and typically occur at a time-scale which is out of reach for simulations. In this work, we introduce a system of particles coupled with a slow macroscopic external variable which approximately follows a Langevin dynamics associated to a coarse-grained free energy. The empirical distribution of the particle system thus samples all local minimisers of the initial free energy, with transition times which are now independent from the number of particles. The construction is inspired by a theoretical tool: the two-scale approach for proving log-Sobolev inequalities for Gibbs measures.
