ITR: Computational Theory and Tools for Reduced-Order Modeling of Very Large Dynamical Systems and Applications

对各种应用中产生的物理系统的动态行为进行准确和有效的模拟的持续和迫切的需求导致了越来越大和复杂的模型。降阶建模（ROM），也称为模型简化，技术在提供有效的计算原型工具以近似较小的模型代替此类大规模模型方面发挥着不可或缺的作用。这样的降阶模型必须能够捕捉关键的动力学行为，并忠实地保留他们近似的更大的模型的基本属性。准确有效的降阶模型可用于大规模模型及其仿真的物理系统的稳态分析、瞬态分析或灵敏度分析。因此，科学家和工程师可以大大减少设计时间，并追求更积极的设计策略。设计师可以尝试``如果”的实验在几个小时内，而不是days.In这个提案中，我们提出了广泛的协同研究活动的ROM有关的三个相互联系的链：计算理论，可靠的算法，和高性能的软件工具。我们还将积极参与促进ROM技术的应用，并通过与电路模拟，结构动力学，控制系统和微机电系统（MEMS）研究人员的现有和新的合作来测试我们的方法。具体而言，我们提出的计算理论和算法的研究活动包括：在时域和频域的精度估计。使用ROM和统计条件估计技术进行线性系统的灵敏度分析。开发直接利用所谓的二阶模型结构并以二阶形式生成降阶模型的ROM技术。探索ROM技术的某些类型的大型非线性系统的技术重要性的框架。

The continual and compelling need for accurately and efficiently simulating dynamical behavior of physical systems arising from a wide variety of applications has led to increasingly large and complex models. Reduced-order modeling (ROM), also called model reduction, techniques play an indispensable role in providing efficient computational prototyping tools to replace such large-scale models by approximate smaller models. Such reduced-order models must be capable of capturing critical dynamical behavior and faithfully preserving essential properties of the larger models they approximate. An accurate and effiective reduced-order model can be applied for steady-state analysis, transient analysis, or sensitivity analysis of large-scale models and the physical systems they emulate. Consequently, scientists and engineers can significantly reduce design time and pursue more aggressive design strategies. Designers can try ``what-if" experiments in hours instead of days.In this proposal, we propose a broad range of synergistic research activities on ROM relating to three interlinking strands: computational theory, reliable algorithms, and high-performance software tools. We will also be actively involved with promoting applications of ROM techniques and testing our methods through existing and new collaborations with researchers in circuit simulation, structural dynamics, control systems, and microelectromechanical systems (MEMS). Specifically, our proposed research activities on computational theory and algorithms include: Accuracy estimation in both time and frequency domains. Sensitivity analysis of linear systems using the techniques of ROM and statistical condition estimation. Development of ROM techniques that directly exploit so-called second-order model structures and generate a reduced-order model in second-order form. Exploration of a framework of ROM techniques for certain types of large-scale nonlinear systems of technological importance.