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

William Marsh Rice University, Houston TX

Investigators

Abstract

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.