PDE-constrained Optimization under Uncertainty

Journal Article · Wed Nov 01 00:00:00 EDT 2017 · SIAG/OPT Views and News

OSTI ID:1429698

Kouri, Drew Philip ^[1]; Surowiec, Thomas Michael ^[2]

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1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2. Philipps-Univ. Marburg (Germany)

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.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC04-94AL85000
• OSTI ID: 1429698
• Report Number(s): SAND--2017-12775J; 659023
• Journal Information: SIAG/OPT Views and News, Journal Name: SIAG/OPT Views and News Journal Issue: 2 Vol. 23; ISSN 9999-0050
• Publisher: SIAM Activity Group on Optimization
• Country of Publication: United States
• Language: English

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