New Strategies for Efficient Monte Carlo Simulation

这笔赠款为开发一种新的高效蒙特卡罗模拟方法提供资金，称为结构化数据库蒙特卡罗(SDMC)。SDMC与蒙特卡罗模拟的常见实现有很大的不同，需要不同的计算体系结构。它适用于目标是对系统或问题(包括灵敏度估计和优化)进行参数研究的模拟项目，该系统或问题需要在潜在的大量参数值下进行性能评估。通过蒙特卡罗对期望(平均值)的评估可以被视为评估多维(通常是非常高维度)的积分。SDMC将这一集成问题转化为一维或几乎一维的集成问题。该项目将涉及开发新的方差减少或其他有效的蒙特卡罗算法，对所提议的算法进行理论分析，并仔细研究新的实现架构意味着什么以及如何最好地执行它。如果研究成功，蒙特卡罗模拟的广泛适用性将对计算科学和实践产生重大影响。虽然该方法应用非常广泛，但该项目的重点将放在由布朗运动或泊松过程的矢量驱动的模型上。这些模型被广泛应用，包括计算金融、计算物理和网络模拟，仅举几例。此外，还将组织一次关于高效蒙特卡洛技术的讲习班。

This grant provides funding for the development of a new efficient Monte Carlo simulation method, called Structured Database Monte Carlo (SDMC). SDMC represents a substantial departure from common implementations of Monte Carlo simulation and requires a different architecture of computation. It is intended for simulation projects whose goal is a parametric study of a system or a problem (including sensitivity estimation and optimization) that requires performance evaluations at a potentially large number of parameter values. Evaluation of expectations (averages) via Monte Carlo can be viewed as evaluating a multi-dimensional (often of a very high dimension) integral. SDMC turns this integration problem into one of a single-dimensional or almost single-dimensional integration. The project will involve the development of new variance reduction or other efficient Monte Carlo algorithms, theoretical analyses of the proposed algorithms, and a careful study of what the new implementation architecture implies and how it can be best carried out. Particular attention and effort will be devoted to implementations on high-performance computing platforms needed for very large computational problems.If successful, the research will have a significant impact on computational science and practice due to the wide applicability of Monte Carlo simulation. While the methodology is very widely applicable, the focus of the project will be on models that are driven by vectors of Brownian motion or Poisson processes. These models are used in a broad range of applications, including computational finance, computational physics, and network simulation, to name a few. In addition, a workshop on Efficient Monte Carlo Techniques will be organized.