AF:Small: Data-Driven Dimension Reduction of Linear and Nonlinear Systems

AF:Small：数据驱动的线性和非线性系统降维

• 批准号: 1320866
• 负责人: Danny Sorensen
• 金额: $ 40万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1320866&HistoricalAwards=false
• 关键词: AF; Small; Data; Driven; Dimension

Large-scale simulations lead to overwhelming demands on computational resources, the main motivation for model reduction. One seeks to produce a reduced-order model which approximates the original one as accurately as possible, making the simulations much faster and cheaper, while preserving appropriate properties. Model reduction is essential for numerous large scale simulations that require many many runs of the same model at slightly different parameter settings.This project has two major themes that address serious computational issues for linear and nonlinear model reduction. The first problem has to do with the stability and/or passivity preservation in model reduction of large-scale systems. This takes place in the newly developed Loewner or data-driven framework. The second involves extensions of the DEIM approach to nonlinear model reduction. The techniques developed recently by the investigators have been utilized in a number of areas including: numerous Navier Stokes CFD applications, turbulent flows, shallow water equations; nonlinear elliptic-parabolic systems for modeling lithium-ion batteries; electrical, thermal and micro-electromechanical systems; complex engineering and geophysical flows; finite elastodynamics; nonlinear fracture mechanics, cardiac electrophysiology; reduced order quadrature; neural modeling; production optimization of oil reservoirs; and many others.

大规模模拟导致对计算资源的压倒性需求，这是模型简化的主要动机。人们试图产生一个降阶模型，它尽可能准确地近似原始模型，使模拟更快，更便宜，同时保持适当的属性。 模型简化对于许多大规模的模拟是必不可少的，这些模拟需要在稍微不同的参数设置下运行许多相同的模型。这个项目有两个主要的主题，解决线性和非线性模型简化的严重计算问题。第一个问题与大系统模型降阶中的稳定性和/或无源性保持有关。这发生在新开发的Loewner或数据驱动框架中。 第二个涉及扩展的DEIM方法的非线性模型减少。研究人员最近开发的技术已被用于许多领域，包括：众多的Navier Stokes CFD应用，湍流，浅水方程;用于模拟锂离子电池的非线性椭圆抛物系统;电气，热和微机电系统;复杂的工程和地球物理流;有限弹性动力学;非线性断裂力学，心脏电生理学;降阶求积;神经建模;油藏的生产优化;以及许多其他。