Mathematical Sciences: Advanced Computational Stochastic Dynamic Programming for Continuous Time Problems

研究者和同事开发了先进的计算方法来解决不确定环境中的大规模动态规划问题。这些方法包括在大规模并行和海量存储处理器上进行并行计算、图形可视化、问题映射、内存管理和数据重构等，以解决普通方法无法解决的大维度问题。目标是开发快速算法，用于大型，一般，连续时间，非线性，随机动力系统的最优反馈控制，同时受到高斯和分布泊松白噪声的干扰。处理泊松过程的随机跳变来模拟罕见的灾难性事件是本研究的一个特殊和具有挑战性的特点。本研究的主要应用是不确定环境下地下水水质的最优修复。其他应用是部分观察控制系统中的参数不确定性，即双重控制问题，以及准时制制造系统。研究人员的数值方法直接处理随机动态规划的偏微分方程。新的算法，如空间和状态有限元，被用来减轻内存和计算需求。基于智能状态空间搜索的纯并行算法也正在开发中。图形可视化和数据管理工具的开发对于在多个维度上分析大量输出是必不可少的。当存在不确定性时，研究者和同事正在开发环境和制造问题的最佳解决方案。问题中不确定性原因的例子是环境中意外引入的污染和未知参数，而在制造的情况下，一个例子是机器的随机故障。寻求最优解的原因是为了最小化成本或浪费宝贵的材料或资源。研究者研究的一个大而重要的应用是污染来源或地下状态不确定的地下水资源的清理。由于地下水污染场地的成本可能从数百万到数十亿甚至更多（有些场地的清理程序未知），最佳解决方案可以比现有的次优程序节省数百万美元。通过优化管理的准时制制造系统也可以获得类似的节省，从而增强我们的全球竞争力。研究人员及其同事开发了先进的计算技术，使用高性能计算来计算最佳解决方案，这在不确定的环境或参数使解决方案的计算量非常大时至关重要。高性能计算包括使用大型计算机来快速优化解决方案和图形可视化，以使大量的输出可以理解，例如环境资源或制造工厂经理，他们将是主要用户。

Hanson 9626692 The investigator and associates develop advanced computational methods to solve large scale dynamic programming problems in uncertain environments. These methods include parallel computation, graphical visualization, problem mapping, memory management and data restructuring on massively parallel and massive memory processors to solve large dimensional problems that could not be solved by ordinary methods. The objective is develop fast algorithms for the optimal feedback control of large, general, continuous time, nonlinear, stochastic dynamical systems, perturbed by both Gaussian and distributed Poisson white noise. The treatment of the random jumps of Poisson processes for modeling rare, disastrous events is a special and challenging feature of this research. The main application of this research is to optimal remediation for groundwater quality in an uncertain environment. Other applications are to parameter uncertainty in partially observed control systems, i.e., the dual control problem, and to just-in-time manufacturing systems. The numerical approach of the investigators directly treats the partial differential equation of stochastic dynamic programming. New algorithms, such as spatial and state finite elements, are used to alleviate both memory and computational demands. Purely parallel algorithms based on intelligent state space search are also being developed. The development of graphical visualization and data management tools are essential for analyzing massive amounts of output in many dimensions. The investigator and associates are developing optimal solutions to environmental and manufacturing problems when there is some uncertainty involved. Examples of the cause of uncertainty in the problem are the unexpected introduction of pollution and unknown parameters in the case of the environment, while in the case of manufacturing an example would be the random failure of machines. The reason for seeking optimal solutio ns is to minimize costs or wasting precious materials or resources. A large and important application that the investigator studies is the cleanup of groundwater resources where the source of the pollution or the underground state is uncertain. Since polluted groundwater sites can costs from millions to billions and more (there are some sites for which cleanup procedures are unknown), optimal solutions could save millions over existing sub-optimal procedures. Similar savings can be obtained for just-in-time manufacturing systems that are optimally managed, enhancing our globally competitive capabilities. The investigator and associates develop advanced computing techniques to compute the optimal solutions using high performance computing, which is essential when uncertain environments or parameters make the amount of computation for the solution very large. The high performance computing involves using massive computers for fast optimal solutions and graphical visualization to make the immense amount of output understandable, for instance to the environmental resource or manufacturing plant manager who would be the prime user.