Making the best of a bad situation: a multiscale approach to free energy calculation

Many enhanced sampling techniques rely on the identification of a number of collective variables that describe all the slow modes of the system. By constructing a bias potential in this reduced space one is then able to sample efficiently and reconstruct the free energy landscape. In methods like metadynamics, the quality of these collective variables plays a key role in convergence efficiency. Unfortunately in many systems of interest it is not possible to identify an optimal collective variable, and one must deal with the non-ideal situation of a system in which some slow modes are not accelerated.
We propose a two-step approach in which, by taking into account the residual multiscale nature of the problem, one is able to significantly speed up convergence. To do so, we combine an exploratory metadynamics run with an optimization of the free energy difference between metastable states, based on the recently proposed variationally enhanced sampling method. This new method is well parallelizable and is especially suited for complex systems, because of its simplicity and clear underlying physical picture.

诸多增强采样（enhanced sampling）技术均依赖于对若干集体变量（collective variables）的识别，这些变量可刻画体系的所有慢模式。通过在该约化空间中构建偏置势，即可实现高效采样并重构自由能景观（free energy landscape）。在元动力学（metadynamics）这类方法中，此类集体变量的质量对收敛效率起着关键作用。然而在诸多受关注的体系中，无法识别出最优的集体变量，此时不得不面对部分慢模式未被加速的非理想场景。
我们提出了一种两步法策略，通过考量该问题残留的多尺度特性，可显著加快收敛速度。为此，我们结合了探索性元动力学运行流程与亚稳态（metastable states）间自由能差（free energy difference）的优化过程，该优化基于近期提出的变分增强采样（variationally enhanced sampling）方法。该新方法具备良好的可并行性，且因其简洁性与清晰的底层物理图像，尤其适用于复杂体系。