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

大规模模拟导致对计算资源的巨大需求，这是模型简化的主要动机。一种方法是建立一个尽可能精确地接近原始模型的降阶模型，使模拟更快、更便宜，同时保留适当的性质。模型简化对于许多大规模模拟是必不可少的，这些模拟需要在稍微不同的参数设置下对同一模型进行多次多次运行。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简化中的稳定性和/或被动性保持有关。这发生在新开发的Loewner或数据驱动框架中。第二部分涉及将DEIM方法扩展到非线性模型约简。研究人员最近开发的技术已在许多领域得到应用，包括：许多Navier Stokes CFD应用、湍流、浅水方程；锂离子电池非线性椭圆-抛物系统建模电气、热力和微机电系统；复杂工程和地球物理流；有限的弹性动力学;非线性断裂力学，心脏电生理；降阶正交；神经建模;油藏生产优化；还有其他许多人。

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.