在微宏马尔科夫链的蒙特卡洛方法中,假边际近似的自由能量
Hannes Vandecasteele1,2, Giovanni Samaey2
1Department of Chemical and Biomolecular Engineering, Johns Hopkins University, 3400 N. Charles Street Baltimore, Maryland 21218, USA.
The Journal of chemical physics
|March 11, 2024
概括
我们开发了一种新的微宏马尔科夫链蒙特卡洛 (mM-MCMC) 方法,用于更快的分子模拟. 这种方法通过使用伪边际近似来加快微观吉布斯分布的采样,从而降低了计算成本.
科学领域:
- 计算化学的计算化学
- 统计力学 统计力学
- 分子动力学分子动力学
背景情况:
- 马尔科夫链蒙特卡洛 (MCMC) 方法对于采样分子配置至关重要.
- 在宏观和微观动态之间进行时间尺度分离的加速模拟仍然是一个挑战.
- 以前的微宏MCMC方法需要准确的自由能量近似值,这限制了它们的计算效率.
研究的目的:
- 引入一个通用的微宏马尔科夫链蒙特卡洛 (mM-MCMC) 方法.
- 消除与mM-MCMC. 的自由能量近似相关的计算瓶.
- 为了加快微观吉布斯分布在时间尺度分离的系统中的采样.
主要方法:
- 一般化的mM-MCMC方法涉及提出宏观反应坐标值,宏观接受/拒绝步骤,微观实例的偏向模拟和微观接受/拒绝步骤.
- 使用假边际近似的自由能量来降低计算成本.
- 该方法在具有低维反应坐标的分子系统上得到说明.
主要成果:
- 伪边际近似显著降低了微观接受/拒绝步骤的计算成本.
- 尽管近似,mM-MCMC方法提供了公正的样本.
- 该方法证明了对具有时间尺度分离的系统进行微观吉布斯分布的有效采样.
结论:
- 带有伪边际近似的通用mM-MCMC方法为分子模拟提供了一个计算效率高的方法.
- 这种方法克服了以前的mM-MCMC技术的局限性,消除了对准确的自由能量计算的需求.
- 开发的技术适用于具有不同时间尺度的各种分子系统.
相关概念视频
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
54
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
54
01:23Mechanistic Models: Compartment Models in Individual and Population Analysis
40
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
40
02:49Calculating Standard Free Energy Changes
21.3K
The free energy change for a reaction that occurs under the standard conditions of 1 bar pressure and at 298 K is called the standard free energy change. Since free energy is a state function, its value depends only on the conditions of the initial and final states of the system. A convenient and common approach to the calculation of free energy changes for physical and chemical reactions is by use of widely available compilations of standard state thermodynamic data. One method involves the...
21.3K
01:22Mean free path and Mean free time
3.6K
Consider the gas molecules in a cylinder. They move in a random motion as they collide with each other and change speed and direction. The average of all the path lengths between collisions is known as the "mean free path."
3.6K
02:39Gibbs Free Energy
33.4K
One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...
33.4K
02:23Gibbs Free Energy and Thermodynamic Favorability
6.8K
The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:
6.8K