Brownian bridges for stochastic problems in chemical sciences

化学科学中随机问题的布朗桥

• 批准号: 2126230
• 负责人: Vivek Narsimhan
• 金额: $ 29.45万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-10-01 至 2024-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2126230&HistoricalAwards=false
• 关键词: Brownian; bridges; stochastic; problems; chemical

Continuous random walks – noisy processes that drift in time – are omnipresent in a wide range of chemical fields such as in studying polymer molecule dynamics, identifying chemical reaction pathways, and quantifying heat and mass transfer processes at the molecular scale. In many practical situations, one is interested in examining random walks whose paths start and end within specified sets of values that represent distinct chemical species or molecule configurations. Such ideas would allow one to quantify rare events in a chemical process, or conversely, quantify the most probable configurations and reaction pathways. One promising methodology to systematically generate these random walks is to make use of a concept known as a stochastic bridge, an idea that has been used in chemical process control theory to guide noisy processes to safe and profitable end states. However, this idea has yet to be adapted to applications in chemistry despite its potential for a wide range of applications in polymer physics and molecular simulations. This proposal formulates stochastic bridges for two chemistry applications where traditional techniques to account for the noise are computationally inefficient. The first application considers the growth of semi-flexible polymer chains of a specific configuration, which is useful when studying DNA molecule behavior during biochemical processes. The second application focuses on efficiently examining different reaction pathways during crystallization, which is vital for manufacturing pharmaceuticals. The investigators will disseminate their results through national conferences and will provide science demonstrations to a local science museum that will revolve around the theme of random walks.To computationally study the wide range of molecular-scale chemical processes with dynamics governed by continuous random walks, two primary research objectives will be pursued by the research team. The first objective is to develop highly efficient numerical techniques for stochastic bridges that condition continuous random walks to end in a specified region, stay in a given region, or reach one region before another. Currently, all stochastic bridges are created by solving a Backwards Fokker Planck (BFP) equation, a partial differential equation (PDE), and then using this solution to compute an effective drift that guides paths towards the desired region of phase space. The largest roadblock behind this approach occurs when one cannot readily compute the PDE solution exactly, which is the case for complex or high dimensional systems. The first objective will use the asymptotic properties of the BFP equation to generate an approximate drift that guides random walks to the correct regions of phase space, and determine ways to correct (i.e., re-weight) any errors incurred from this approximation. This procedure will create a computationally efficient method to generate conditioned random walks that can scale to higher dimensions and can be used for complex molecular systems. The second objective will employ these ideas in two applications. The first example will focus on simulating the dynamics of a continuous polymer chain in an external field - a canonical problem in all polymer field theories. The proposed research program will demonstrate that a stochastic bridge can effectively sample polymer conformations that end with a given topology or end with a range of final energies, the latter of which is important for rare event sampling. The second example will consider nucleation pathways during crystallization and will show that a bridge can efficiently sample paths in a free energy landscape that reach one crystal conformation (polymorph) before others, ultimately making it possible to control selectivity between crystal product polymorphs.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

连续随机游走-随时间漂移的噪声过程-在广泛的化学领域中无处不在，例如研究聚合物分子动力学，识别化学反应途径，以及在分子尺度上量化传热和传质过程。在许多实际情况下，人们感兴趣的是研究随机游走，其路径的起点和终点都在代表不同化学物种或分子构型的指定值集合内。这些想法将允许人们量化化学过程中的罕见事件，或者相反，量化最可能的配置和反应途径。一个有前途的方法来系统地产生这些随机游走是利用一个被称为随机桥的概念，一个想法，已被用于化学过程控制理论，以指导噪声过程的安全和有利可图的最终状态。然而，这个想法还没有适应化学中的应用，尽管它在聚合物物理和分子模拟的广泛应用的潜力。该建议制定了两个化学应用的随机桥，传统的技术来考虑噪音是计算效率低下。第一个应用程序考虑了特定配置的半柔性聚合物链的生长，这在生物化学过程中研究DNA分子行为时很有用。第二个应用程序的重点是有效地检查结晶过程中的不同反应途径，这对制药至关重要。研究人员将通过全国性会议传播他们的成果，并将围绕随机游走的主题向当地科学博物馆提供科学演示。为了通过计算研究具有连续随机游走动力学的广泛分子尺度化学过程，研究小组将追求两个主要研究目标。第一个目标是开发高效的随机桥的条件连续随机游动结束在一个指定的区域，留在一个给定的区域，或到达一个区域之前，另一个数值技术。目前，所有的随机桥都是通过求解后向福克-普朗克（BFP）方程、偏微分方程（PDE），然后使用该解计算有效漂移来创建的，该漂移将路径引导到相空间的期望区域。这种方法背后的最大障碍发生在人们不能容易地精确计算PDE解的时候，这是复杂或高维系统的情况。第一个目标将使用BFP方程的渐近性质来生成将随机游走引导到相空间的正确区域的近似漂移，并确定校正（即，重新加权）由该近似引起的任何误差。这个过程将创建一个计算效率高的方法来生成条件随机游走，可以扩展到更高的维度，并可用于复杂的分子系统。第二个目标将在两个应用中使用这些想法。第一个例子将集中在模拟一个连续的聚合物链在外场的动力学-在所有聚合物场论的典型问题。拟议的研究计划将证明，随机桥可以有效地采样聚合物构象，以给定的拓扑结构结束或以一系列最终能量结束，后者对于稀有事件采样很重要。第二个例子将考虑结晶过程中的成核途径，并将表明桥可以有效地采样自由能景观中达到一种晶体构象的路径（多晶型物）之前，该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的评估来支持的。影响审查标准。

项目成果

Brownian bridges for stochastic chemical processes—An approximation method based on the asymptotic behavior of the backward Fokker–Planck equation

随机化学过程的布朗桥 — 基于向后福克渐近行为的近似方法 — 普朗克方程

• DOI: 10.1063/5.0080540
• 发表时间: 2022
• 期刊: The Journal of Chemical Physics
• 作者: Wang, Shiyan;Venkatesh, Anirudh;Ramkrishna, Doraiswami;Narsimhan, Vivek
• 通讯作者: Narsimhan, Vivek