Collaborative Research Model Reduction for Nonlinear and Parametric Systems with Uncertainty

Abstract

This project has developed and analyzed new mathematical algorithms to substantially reduce the complexity of simulating and optimizing parametrically dependent systems and to support decision-making under uncertainty. Specifically, this research has advanced the state of the art in reduced order modeling based on projections and on the discrete empirical interpolation method (DEIM) for nonlinear systems, developed new adaptive sampling methods for optimization of systems with uncertain inputs, devised a domain decomposition based methods to systematically integrate the uncertainty propagation through components into uncertainty propagation through a systems composed of these components, established a so-called CUR factorization based on the DEIM that provides a low rank approximate factorization of a given large matrix with applications to POD model reduction and analysis of data. The feasibility of our algorithms was demonstrated on a number of problems with relevance to the Air Force.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jul 14, 2015
Accession Number
ADA621652

Entities

People

  • Danny C. Sorensen
  • Karen Willcox
  • Matthias Heinkenschloss

Organizations

  • Rice University

Tags

Communities of Interest

  • Autonomy
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Air Force Research Laboratories
  • Algorithms
  • Applied Mathematics
  • Computational Science
  • Data Analysis
  • Data Science
  • Decomposition
  • Differential Equations
  • Equations
  • Information Science
  • Machine Learning
  • Nonlinear Systems
  • Partial Differential Equations
  • Random Variables
  • Sampling
  • Two Dimensional

Fields of Study

  • Computer science
  • Engineering

Readers

  • Computational Fluid Dynamics (CFD)
  • Computational Modeling and Simulation
  • Solar Photovoltaics and Thermoelectric Devices.