LCE: Parallel Algorithms for Large-Scale Simulation-Based Optimization

9732301 Ghattas可扩展的高度并行超级计算机的出现为工程科学中的复杂物理系统建模开辟了新的可能性。在过去的20年里，在偏微分方程（PDE）的并行数值方法的开发、分析和实现方面取得了重大进展，偏微分方程（PDE）控制着许多复杂物理系统的行为。对于工程科学中的许多大类仿真问题，并行算法已经足够成熟，因此可以超越仿真问题，以优化系统所管辖的PDEs.In对比的并行PDE解决方案的大量工作，很少有研究已经进行了并行算法优化的偏微分方程。 然而，考虑到并行偏微分方程求解器的成熟状态，时间已经成熟，可以共同努力开发，分析，实施，应用和研究并行数值方法，以优化由偏微分方程或“基于仿真的优化”控制的系统。“将开发用于解决复杂PDE系统所管理的大规模优化问题的并行算法。 努力将集中在解决两个障碍，出现在非常大规模的优化问题：大量的约束和大量的决策变量。对于前者，将开发内点方法，以解决决策变量增长带来的复杂性;将开发用于最优系统的定制缩减和全空间牛顿-克雷洛夫方法，其中有几种预处理器选择，包括基于缩减海森的无限维近似的预处理器。优化方法将在高度并行的超级计算机上实现，并应用于工程科学中的几个具有挑战性的问题，包括地震波传播的逆问题和生物医学设备的优化设计/控制。

9732301GhattasThe emergence of scalable highly parallel supercomputers has opened up new possibilities for modeling complex physical systems in the engineering sciences. Significant strides have been made over the past 20 years in the development, analysis, and implementation of parallel numerical methods for solution of the partial differential equations (PDEs) that govern the behavior of many of these complex physical systems. For many broad classes of simulation problems in the engineering sciences, parallel algorithms are sufficiently mature so that one may move beyond the simulation problem to optimization of systems governed by PDEs.In contrast to the large body of work on parallel PDE solution, very little research has been conducted on parallel algorithms for optimization of PDEs. However, given the maturing state of parallel PDE solvers, time is ripe to mount a concerted effort to develop, analyze, implement, apply, and study parallel numerical methods for optimization of systems governed by PDEs or "simulation-based optimization."Parallel algorithms for solving large-scale optimization problems governed by complex PDE systems will be developed. Efforts will focus on addressing two barriers that arise in very large scale optimization problems: large numbers of constraints and large numbers of decision variables. For the former, interior point methods will be developed and to address complexity stemming from growth in decision variables; tailor reduced- and full-space Newton-Krylov methods for the optimality system will be developed, with several choices for preconditioners including those based on infinite dimensional approximations of the reduced Hessian. The optimization methods will be implemented on highly parallel supercomputers, and applied to several challenging problems in engineering science, including inverse problems in seismic wave propagation and optimal design/control of biomedical devices.***