Efficient Monte Carlo Methods for Nonequilibrium Statistical Physics

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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.