(YIP) ADAPTIVE, DATA-DRIVEN MODEL REDUCTION AND MACHINE LEARNING TO ENABLE HIGH-FIDELITY, MANY-QUERY COMPUTATIONAL PHYSICS
Abstract
For the past decade, projection-based reduced-order models, which project the dynamics of a largescale system onto a low-dimensional subspace derived from data, have been prophesied as a game-changing technology needed to enable the rapid solution of large-scale challenge problems. While reduced-order models have demonstrated exceptional speed-up, they lack parametric robustness, which has prevented them from delivering the promised technology. We propose a fundamentally new numerical framework that is a hybrid between model reduction and traditional discretization methods, where reliable error estimation and adaptivity will be central to achieve robustness. The method will use basis functions with global support to represent the solution, similar to reduced-order models, to achieve a high-degree of accuracy at little computational cost. The solution will be enriched with locally supported basis functions, such as those used in finite element methods, for additional accuracy when the pre-computed global basis is insufficient. Deep neural networks will be used to provide an accurate, efficient, and non-intrusive approximation of nonlinear terms that arise in the discretization. If successful, the research effort will result in a new discretization framework and associated software that can be used to rapidly and robustly run computational simulations to make predictions and inform decisions. It also offers the potential to enable many-query analyses in practical scenarios due to the speed and robustness built-in to the framework.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2021
- Source ID
- FA95502010236
Entities
People
- Matthew Zahr
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Notre Dame