论文标题
通过改编的元动力学改善基于控制的重要性抽样策略
Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics
论文作者
论文摘要
在亚稳态动力学系统中对罕见事件进行采样通常是一项计算昂贵的任务，并且需要诉诸增强的采样方法，例如重要性采样。由于我们可以提出找到最佳重要性采样控制作为随机优化问题的问题，因此这带来了其他数值挑战，相应算法的收敛可能也可能遭受转移。在本文中，我们通过将系统控制方法与启发式适应性元动力学方法相结合来解决这个问题。至关重要的是，我们近似神经网络的重要性采样控制，这使得算法对于高维应用而言是可行的。在相关的亚稳态问题中，我们可以在数值上证明我们的算法比以前的尝试更有效，并且只有两种方法的组合才会导致令人满意的收敛性，从而可以在某些亚稳定设置中进行有效的采样。
Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article, we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high-dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings.
