Fundamental tools for stochastic simulation

我的研究项目涉及基础工具（数学、统计和计算）的开发和研究，用于建模、模拟和优化涉及不确定性的系统。近年来，对改进的仿真工具的需求急剧增加。随机（蒙特卡罗）模拟广泛应用于科学、工程、管理和其他一些领域。模拟通常是处理复杂系统的现实模型的唯一实用工具，这些模型通常是动态的、随机的和非线性的。例如，随机模拟和优化是最近机器学习取得巨大进展的关键因素。

My research program concerns the development and study of fundamental tools (mathematical, statistical, and computational) for modeling, simulating, and optimizing systems that involve uncertainty. The demand for improved simulation tools has increased tremendously in recent years. Stochastic (Monte Carlo) simulation is used heavily in science, engineering, management, and several other areas. Simulation is often the only practical tool to deal with realistic models of complex systems, which are typically dynamic, stochastic, and nonlinear. Stochastic simulation and optimization have been key ingredients in the spectacular recent progress in machine learning, for example. My goal in this context is to contribute new ideas and methods to the Monte Carlo tool set, and improve our understanding of the existing ones. I contribute to theoretical aspects (such as convergence analysis of simulation algorithms and mathematical analysis of the structure of random number generators) and practical ones (e.g., empirical experimentation, software implementation, and adaptation to specific real-life applications). My main focus in on general tools that have a wide range of applications, such as random number and random variate generators, quasi-Monte Carlo methods, variance-reduction methods, rare-event simulation techniques, and stochastic optimization methods. I also work on selected applications, e.g., in finance, reliability, and management of service systems. The main directions of my research, currently and over the next five years, are: (1) study and improve the methods for generating (pseudo)random numbers for simulation on various types of platforms, in particular for massively-parallel computers, and methods to test such generators; (2) develop and study randomized quasi-Monte Carlo (RQMC) methods, which replace the independent vectors of random numbers used in Monte Carlo (MC) simulations by points that cover the space more uniformly than random points, to improve accuracy, and provide effective practical tools that implement these methods; (3) design and study efficient rare-event simulation methods, for settings in which certain events that occur very rarely have a large impact on the performance measure of interest, and study applications of these; (4) develop simulation-based optimization methods for decision making in complex stochastic systems; (5) develop effective methods to build stochastic models of complex service systems that involve humans, based on large amounts of data, to support decision making (e.g., emergency services, call centers, healthcare systems, finance, network economics for the Internet, reliability problems, etc.).