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

高性能计算对于在航空航天、结构、资源、经济和机器人等大规模应用的优化控制中管理大量计算和内存需求至关重要。实现先进的计算技术，如并行化，矩阵化（包括向量化），图形可视化和问题映射使得解决更大维度的问题成为可能。我们的研究目标是开发一般连续时间非线性随机动力系统最优反馈控制的快速算法。这些系统包括高斯和分布泊松白噪声的扰动。先进的计算处理这些系统，特别是与泊松噪声，是一个特别独特的特点，这一建议。这些算法正在多状态资源模型上进行测试，但适用于各种各样的应用。数值方法直接处理随机规划的偏微分方程。新的算法，如有限元，将被开发出来，以减轻内存和计算密集型的需求，从“维度的诅咒”。纯并行方法正在开发用于可扩展、大规模并行和大容量存储的超级计算机，包括新一代“超级计算机”。图形可视化工具的开发对于在多个维度上分析大量输出也是必不可少的。还有一些相关的问题。* * *

9301107 Hanson High performance computing is essential for managing massive computational and memory demands in optimal control of large scale applications, such as aerospace, structures, resources, economics and robotics. Implementation of advanced computational techniques, such as parellelization, matrization (including vectorization), graphical visualization and problem mapping make possible the solution of larger dimensional problems. Our research objective is to develop fast algorithms for the optimal feedback control of general continuous time nonlinear stochastic dynamical systems. These systems include perturbations by both Gaussian and distributed Poisson white noise. Advanced computational treatment of these systems, especially with Poisson noise, is a particularly unique feature of this proposal. The algorithms are being testing on multi-state resource models, but are applicable to a wide variety of applications. The numerical approach directly treats the partial differential equation of stochastic programming. New algorithms, such as finite element, will be developed to alleviate both memory and computationally intensive demands from the "curse of dimensionality". Purely parallel methods are being developed for scalable, massively parallel and massive memory supercomputers, including new generation "ultracomputers". The development of graphical visualization tools is also essential for analyzing massive amounts of output in many dimensions. There are also several related problems as well. ***