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

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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.