DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: PDE-constrained Optimization under Uncertainty

Abstract

Uncertainty is pervasive in all science and engineering applications. Incorporating uncertainty in physical models is therefore both natural and vital. In doing so, we often arrive at parametric systems of partial differential equations (PDEs). When passing from simulation to optimization, we obtain (typically nonconvex) infinite-dimensional optimization problems that, upon discretization, result in extremely large-scale nonlinear programs. For example, consider a linear elliptic PDE on a two- dimensional domain with a single random coeffcient. If we sampled the random input with 10,000 realizations of the coeffcient, the resulting optimization problem would have 10,000 PDE constraints. Furthermore, discretizing each PDE with piecewise linear finite elements on a 100X100 uni- form quadrilateral mesh results in 100,000,000 degrees of freedom. As a result, the critical components for ensuring mesh-independent performance of numerical optimization methods in the deterministic setting, for example, solution regularity and generalized differentiability, are even more critical in the stochastic setting.

Authors:
 [1];  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Philipps-Univ. Marburg (Germany)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1429698
Report Number(s):
SAND-2017-12775J
Journal ID: ISSN 9999-0050; 659023
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Accepted Manuscript
Journal Name:
SIAG/OPT Views and News
Additional Journal Information:
Journal Volume: 23; Journal Issue: 2; Journal ID: ISSN 9999-0050
Publisher:
SIAM Activity Group on Optimization
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING

Citation Formats

Kouri, Drew Philip, and Surowiec, Thomas Michael. PDE-constrained Optimization under Uncertainty. United States: N. p., 2017. Web.
Kouri, Drew Philip, & Surowiec, Thomas Michael. PDE-constrained Optimization under Uncertainty. United States.
Kouri, Drew Philip, and Surowiec, Thomas Michael. Wed . "PDE-constrained Optimization under Uncertainty". United States. https://www.osti.gov/servlets/purl/1429698.
@article{osti_1429698,
title = {PDE-constrained Optimization under Uncertainty},
author = {Kouri, Drew Philip and Surowiec, Thomas Michael},
abstractNote = {Uncertainty is pervasive in all science and engineering applications. Incorporating uncertainty in physical models is therefore both natural and vital. In doing so, we often arrive at parametric systems of partial differential equations (PDEs). When passing from simulation to optimization, we obtain (typically nonconvex) infinite-dimensional optimization problems that, upon discretization, result in extremely large-scale nonlinear programs. For example, consider a linear elliptic PDE on a two- dimensional domain with a single random coeffcient. If we sampled the random input with 10,000 realizations of the coeffcient, the resulting optimization problem would have 10,000 PDE constraints. Furthermore, discretizing each PDE with piecewise linear finite elements on a 100X100 uni- form quadrilateral mesh results in 100,000,000 degrees of freedom. As a result, the critical components for ensuring mesh-independent performance of numerical optimization methods in the deterministic setting, for example, solution regularity and generalized differentiability, are even more critical in the stochastic setting.},
doi = {},
journal = {SIAG/OPT Views and News},
number = 2,
volume = 23,
place = {United States},
year = {2017},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
The DOI is not currently available

Save / Share: