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.
