快速准确的多维自由能积分
Fast and accurate multidimensional free energy integration
摘要：
热力学积分系列的增强采样和自由能计算算法（例如自适应偏置力方法，ABF）不是基于自由能表面的直接计算，而是基于其梯度。积分自由能表面在高于一的维度上是不平凡的。在这里，作者介绍了一个灵活的，便携式的实现泊松方程形式主义集成自由能表面估计梯度在2和3维，使用任何组合的周期性和非周期性（诺依曼）边界条件。该算法在便携式C++中实现，并作为一个独立的工具提供，可用于集成使用任何算法在网格上估计的多维梯度场，例如伞积分作为伞采样模拟的后处理。它也包含在集合变量模块中的ABF（及其扩展系统变体eABF）的实现中，使ABF和eABF模拟中的多维自由能表面的无缝计算成为可能。提供了一个基于Python的分析工具链，可以轻松地绘制和分析多维ABF模拟结果，包括评估其收敛性的指标。泊松积分算法也可以用于执行Helmholtz分解的噪声梯度估计的飞行，从而有效地实现了投影ABF（pABF）方法提出的Lelièvre和同事。在数值试验中，pABF被发现导致更快的收敛相对于ABF在简单的情况下，低的内在维度，但似乎不利于收敛在一个更现实的情况下，涉及退化坐标和隐藏的障碍，由于较慢的探索。这表明，方差减少计划并不总是产生收敛性的改善时，应用于增强的采样方法。
英文摘要：
Enhanced sampling and free energy calculation algorithms of the Thermodynamic Integration family (such as the Adaptive Biasing Force method, ABF) are not based on the direct computation of a free energy surface, but rather of its gradient. Integrating the free energy surface is non-trivial in dimension higher than one. Here the author introduces a flexible, portable implementation of a Poisson equation formalism to integrate free energy surfaces from estimated gradients in dimension 2 and 3, using any combination of periodic and non-periodic (Neumann) boundary conditions. The algorithm is implemented in portable C++, and provided as a standalone tool that can be used to integrate multidimensional gradient fields estimated on a grid using any algorithm, such as Umbrella Integration as a post-treatment of Umbrella Sampling simulations. It is also included in the implementation of ABF (and its extended-system variant eABF) in the Collective Variables Module, enabling the seamless computation of multidimensional free energy surfaces within ABF and eABF simulations. A Python-based analysis toolchain is provided to easily plot and analyze multidimensional ABF simulation results, including metrics to assess their convergence. The Poisson integration algorithm can also be used to perform Helmholtz decomposition of noisy gradients estimates on the fly, resulting in an efficient implementation of the projected ABF (pABF) method proposed by Lelièvre and co-workers. In numerical tests, pABF is found to lead to faster convergence with respect to ABF in simple cases of low intrinsic dimension, but seems detrimental to convergence in a more realistic case involving degenerate coordinates and hidden barriers, due to slower exploration. This suggests that variance reduction schemes do not always yield convergence improvements when applied to enhanced sampling methods.
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