CAREER: Reduced-order Modeling and Controller Design for Large-scale Dynamical Systems via Rational Krylov Methods

提案ID：0645347 PI：Gugercin，Serkan机构：Virginia Polytechnic Institute and State UniversityTitle：CAREER：Reduced-Order Modeling and Controller Design for Large-scale Dynamical Systems via Rational Krylov MethodsAbstractDirect numerical simulation of dynamic systems has been one of the few available means for achieving accurate prediction or control of complex physical phenomena that are of scientific interest or industrial value.不断增长的精度需求导致非常大规模和复杂的动力系统。在如此大规模的环境中进行模拟会使计算资源不堪重负;这是模型简化的主要动机。我们的目标是产生一个更简单的降阶模型，尽可能准确地逼近原始模型。然后，所得到的简化模型可以用作原始模型的有效替代，以在更大的仿真中替换它，或者开发适合于真实的应用的更简单和更快的控制器。基于Krylov的方法已成为现实大规模环境中模型约简的有前途的候选方法。该项目旨在开发最佳，鲁棒和系统的基于Krylov的投影方法，用于高效构建高保真和最佳降阶模型。通过在基于Krylov的模型降阶设置中小心地采用不精确解，所提出的研究将这些最优降阶技术扩展到具有数百万自由度的现实设置，同时保持相对于精确有理Krylov子空间的误差测量的相同质量。此外，系统的方法将开发的快速和有效的，低阶最优控制器的设计，更一般地说，减少互连（耦合）系统。该项目将把新开发的方法应用于来自不同应用领域的几个测试问题。大规模模拟和计算在研究计算科学和工程的许多领域中的各种复杂物理现象方面发挥着至关重要的作用。例子包括电路中的信号传播和干扰、分子动力学、天气预报、大型结构中的波传播和振动抑制、各种介质中的温度控制以及微机电系统的行为。在大规模的设置计算导致无法管理的国家的计算资源的巨大需求，因此有一个越来越多的需要近似复杂的动力系统与简单，高保真度的模型，这将使这些模拟更容易和更快地计算。该项目旨在开发技术，以产生复杂系统的最佳，高保真度近似;立即导致更快速但仍然可靠的模拟。通过本项目开发的数学工具和高质量软件将有助于科学家和工程师处理大规模复杂的多物理问题的研究工作。除了研究部分，该项目还提供了一个全面的教育计划，包括对本科生和研究生的监督;研究生课程的开发;以及几个跨学科的研究项目，可用于向学生介绍高性能科学计算的各个领域。

Proposal ID: 0645347PI: Gugercin, SerkanInstitution: Virginia Polytechnic Institute and State UniversityTitle: CAREER: Reduced-order Modeling and Controller Design for Large-scale Dynamical Systems via Rational Krylov MethodsAbstractDirect numerical simulation of dynamical systems has been one of the few available means for achieving accurate prediction or control of complex physical phenomena that are of scientific interest or industrial value. The ever-increasing need for improved accuracy leads to very large-scale and complex dynamical systems. Simulations in such large-scale settings can overwhelm computational resources; this is the main motivation for model reduction. The goal is to produce a simpler reduced-order model approximating the original one as accurately as possible. The resulting reduced model can then be used as an efficient surrogate to the original, to replace it in a larger simulation or to develop a simpler and faster controller suitable for real time applications. Krylov-based methods have emerged as promising candidates for model reduction in realistic large-scale settings. This project seeks to develop optimal, robust, and systematic Krylov-based projection methods for efficient construction of high fidelity and optimal reduced-order models. By carefully employing inexact solves in a Krylov-based model reduction setting, the proposed research will extend these optimal reduction techniques to realistic settings with millions of degrees of freedom while maintaining the same quality of the error measures with respect to the exact rational Krylov subspaces. In addition, systematic approaches will be developed for the design of fast and effective, low-order optimal controllers, and more generally, for reduction of interconnected (coupled) systems. The project will apply the newly developed methods to several test problems drawn from different application areas.Large-scale simulations and computations play a crucial role in studying a great variety of complex physical phenomena in many areas of computational science and engineering. Examples include signal propagation and interference in electric circuits, molecular dynamics, weather forecasting, wave propagation and vibration suppression in large structures, temperature control in various media, and behavior of micro-electro-mechanical systems. Computing in large-scale settings leads to unmanageably large demands on the nation's computational resources; hence there is a growing need to approximate the complex dynamical systems with simpler, high fidelity models that will make these simulations much easier and faster to compute. This project seeks to develop techniques that will yield optimal, high fidelity approximations of complex systems; leading at once to simulations that are more rapid yet still reliable. The mathematical tools and high-quality software that will be developed through the course of this project will contribute to research efforts of scientist and engineers working with large-scale, complex multi-physics problems. In addition to the research component, this project offers a comprehensive education plan that consists of the supervision of undergraduate and graduate students; development of a graduate course; and several interdisciplinary research projects available for introducing students in a variety of areas of high-performance scientific computing.