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。我在这方面的目标是为蒙特卡罗工具集提供新的想法和方法，并提高我们对现有工具集的理解。我在理论方面（如模拟算法的收敛分析和随机数生成器结构的数学分析）和实践方面（如经验实验，软件实现和适应具体的现实应用）做出了贡献。我主要关注具有广泛应用的通用工具，如随机数和随机变量生成器、准蒙特卡罗方法、方差缩减方法、罕见事件模拟技术和随机优化方法。我也从事一些特定的应用，如金融、可靠性和服务系统管理。我目前和未来五年的主要研究方向是：(1)研究和改进在各种类型的平台上，特别是在大规模并行计算机上模拟的（伪）随机数的生成方法，以及测试这种生成器的方法；(2)开发和研究随机拟蒙特卡罗（RQMC）方法，将蒙特卡罗（MC）模拟中使用的随机数独立向量替换为比随机点更均匀地覆盖空间的点，以提高精度，并为实现这些方法提供有效的实用工具；(3)设计和研究高效的罕见事件模拟方法，在这种设置中，某些很少发生的事件对感兴趣的性能度量有很大影响，并研究这些方法的应用；(4)开发基于仿真的复杂随机系统决策优化方法；(5)基于大量数据，开发有效方法，构建涉及人类的复杂服务系统的随机模型，以支持决策（如应急服务、呼叫中心、医疗保健系统、金融、互联网网络经济、可靠性问题等）。

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.).