Efficient Monte Carlo Methods for Nonequilibrium Statistical Physics

PI将开发和分析用于模拟非平衡系统的有效计算方法。这项工作将集中在化学中的基本问题，如反应速率的计算。潜在的应用包括药物设计、单分子实验的分析和解释，以及更好地理解调节和维持生命的化学反应网络。国际和平研究所将实施这些方法，并在开源软件中传播它们。该软件将为科学家使用而设计，并将与现有的计算化学软件接口。这项拟议工作的教育部分将把不同群体的高中生带到主办机构的校园里，参加一个数据科学的暑期课程，重点是使用计算机模拟来理解诸如新冠肺炎疫情和陪审团遴选中的种族偏见等问题。这个项目将资助一年级的一名本科生和二年级和三年级的一名研究生。非均衡性可以用来描述两种类型的量：(A)不可逆随机过程的稳态分布的平均值和(B)可逆或不可逆随机过程的动态性质，例如平均首次通过时间。典型的非平衡计算涉及罕见事件。例如，当计算蛋白质的折叠率时，模拟中使用的时间步长可能比折叠事件之间的时间低十个或更多个数量级，从而使直接模拟变得不切实际。然而，经典的稀有事件方法，如重要性抽样，通常不适用于非均衡情况。PI将分析和改进一类新的罕见事件方法，使分层调查抽样的原则适用于非平衡计算。PI基于随机近似和多重网格方法的理论，将提供收敛分析，开发实用的后验误差估计，并确定分层比竞争方法更有效的问题类别。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The PI will develop and analyze efficient computational methods for the simulation of nonequilibrium systems. This work will focus on fundamental problems from chemistry, such as the calculation of reaction rates. Potential applications include drug design, the analysis and interpretation of single-molecule experiments, and the development of a better understanding of the chemical reaction networks that regulate and sustain life. The PI will implement the methods and disseminate them in open-source software. This software will be designed for use by scientists, and will interface with existing computational chemistry software. The educational component of the proposed work will bring diverse groups of high school students onto the campus of the host institution for a summer course in data science emphasizing the use of computer simulations to understand problems such as the COVID-19 pandemic and racial bias in jury selection. This project will support one undergraduate student in year 1 and 1 graduate student each year of years 2 and 3.Nonequilibrium can be used to describe two types of quantities: (a) averages over the steady-state distribution of an irreversible stochastic process and (b) dynamic properties of reversible or irreversible stochastic processes, for example mean first passage times. Typical nonequilibrium calculations involve rare events. For example, when calculating the folding rate of a protein, the time step used in simulation may be ten or more orders of magnitude below the time between folding events, rendering direct simulation impractical. However, classical rare event methods like importance sampling do not usually apply in the nonequilibrium case. The PI will analyze and improve a new class of rare event methods that adapt the principle of stratified survey sampling to nonequilibrium calculations. Building on ideas from stochastic approximation and the theory of multigrid methods, the PI will provide a convergence analysis, develop practical a posteriori error estimates, and identify classes of problems for which stratification is more efficient than competing methods.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.