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-在广泛的化学领域无所不在，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，人们感兴趣的是检查随机行走，其路径在代表不同化学物质或分子构型的指定值集内开始和结束。这样的想法将允许人们量化化学过程中的罕见事件，或者相反，量化最可能的构型和反应途径。一种有希望系统地生成这些随机漫步的方法是利用随机桥的概念，这一概念已被用于化学过程控制理论，以引导有噪声的过程进入安全和有利可图的最终状态。然而，尽管这种想法在聚合物物理和分子模拟中有广泛的应用潜力，但它还没有适应于化学应用。该建议为两种化学应用制定了随机桥，在这些应用中，传统的计算噪声的技术在计算上效率低下。第一个应用考虑了特定构型的半柔性聚合物链的生长，这在研究生物化学过程中的DNA分子行为时很有用。第二个应用侧重于有效地检查结晶过程中的不同反应途径，这对制造药物至关重要。研究人员将通过全国会议传播他们的研究结果，并将在当地一家以随机漫步为主题的科学博物馆进行科学演示。为了计算研究由连续随机游走控制的大范围分子尺度化学过程，研究小组将追求两个主要研究目标。第一个目标是为随机桥开发高效的数值技术，这些随机桥的条件是连续随机行走在指定区域结束，停留在给定区域，或者在另一个区域之前到达一个区域。目前，所有的随机桥都是通过求解一个向后的福克-普朗克（BFP）方程和一个偏微分方程（PDE）来创建的，然后使用这个解来计算一个有效的漂移，该漂移将路径引导到相空间的期望区域。这种方法背后最大的障碍出现在无法准确计算PDE解决方案时，这是复杂或高维系统的情况。第一个目标将使用BFP方程的渐近特性来生成一个近似漂移，该漂移引导随机漫步到相空间的正确区域，并确定纠正（即重新加权）该近似产生的任何误差的方法。该程序将创建一种计算效率高的方法来生成条件随机游走，这种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程序中使用这些想法。第一个例子将着重于模拟连续聚合物链在外场中的动力学，这是所有聚合物场理论中的典型问题。提出的研究计划将证明随机桥可以有效地采样以给定拓扑结束或以最终能量范围结束的聚合物构象，后者对于罕见事件采样很重要。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在自由能景观中采样路径，在其他路径之前到达一个晶体构象（多晶型），最终使控制晶体产物多晶型之间的选择性成为可能。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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