Fundamental tools for stochastic simulation

我的研究项目涉及基本工具（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大幅增加。随机（蒙特卡罗）模拟在科学，工程，管理和其他几个领域中大量使用。仿真通常是处理复杂系统的真实模型的唯一实用工具，这些复杂系统通常是动态的，随机的和非线性的。例如，随机模拟和优化一直是机器学习最近取得惊人进展的关键因素。 我在这方面的目标是为蒙特卡洛工具集贡献新的想法和方法，并提高我们对现有方法的理解。我有助于理论方面（如仿真算法的收敛性分析和随机数生成器结构的数学分析）和实际方面（例如，经验性实验、软件实现和对具体现实应用的适应）。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，稀有事件模拟技术和随机优化方法。我还从事选定应用程序的工作，例如，在金融、可靠性和服务系统管理方面。 目前和今后五年的主要研究方向是：（1）研究和改进在各种平台上，特别是在并行计算机上模拟（伪）随机数的产生方法和测试方法;（2）发展和研究随机拟蒙特卡罗（RQMC）方法，其用比随机点更均匀地覆盖空间的点来代替在蒙特卡罗（MC）模拟中使用的随机数的独立向量，以提高精度，并且提供实现这些方法的有效实用工具;（3）设计和研究有效的稀有事件模拟方法，用于某些事件很少发生的情况下，对感兴趣的性能指标有很大影响的设置，并研究这些方法的应用;（4）开发基于模拟的复杂随机系统决策优化方法;（5）开发有效的方法来建立涉及人类的复杂服务系统的随机模型，基于大量数据，以支持决策（例如，紧急服务、呼叫中心、医疗保健系统、金融、互联网的网络经济、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.).