基于Onsager-Machlup action的路径采样及其与扩散和多路径副本交换的组合
Onsager-Machlup action-based path sampling and its combination with replica exchange for diffusive and multiple pathways
摘要：
为了在崎岖的能源景观中对多条路径进行采样，我们提出了一种新的基于动作的路径采样方法，该方法使用Onsager-Machlup动作泛函。受量子力学系统的Fourier-路径积分模拟的启发，将笛卡尔空间中的路径变换为Fourier空间中的路径，导出了Fourier分量的过阻尼Langevin方程，以实现有限温度下路径的正则系综.为了避免在最初猜测的路径周围的“路径陷阱”，路径采样方法进一步与强大的采样技术副本交换方法相结合。我们的方法的原理和算法的数值演示了一个模型的二维系统与分叉的潜在景观。与传统的过渡路径采样和平衡理论的结果进行了比较，并讨论了由于路径离散化而引起的误差。
英文摘要：
For sampling multiple pathways in a rugged energy landscape, we propose a novel action-based path sampling method using the Onsager-Machlup action functional. Inspired by the Fourier-path integral simulation of a quantum mechanical system, a path in Cartesian space is transformed into that in Fourier space, and an overdamped Langevin equation is derived for the Fourier components to achieve a canonical ensemble of the path at a finite temperature. To avoid "path trapping" around an initially guessed path, the path sampling method is further combined with a powerful sampling technique, the replica exchange method. The principle and algorithm of our method is numerically demonstrated for a model two-dimensional system with a bifurcated potential landscape. The results are compared with those of conventional transition path sampling and the equilibrium theory, and the error due to path discretization is also discussed.
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