Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models
Abstract
Our work presents a method to adaptively refine reduced-order models a posteriori without requiring additional full-order-model solves. The technique is analogous to mesh-adaptive h-refinement: it enriches the reduced-basis space online by ‘splitting’ a given basis vector into several vectors with disjoint support. The splitting scheme is defined by a tree structure constructed offline via recursive k-means clustering of the state variables using snapshot data. This method identifies the vectors to split online using a dual-weighted-residual approach that aims to reduce error in an output quantity of interest. The resulting method generates a hierarchy of subspaces online without requiring large-scale operations or full-order-model solves. Furthermore, it enables the reduced-order model to satisfy any prescribed error tolerance regardless of its original fidelity, as a completely refined reduced-order model is mathematically equivalent to the original full-order model. Experiments on a parameterized inviscid Burgers equation highlight the ability of the method to capture phenomena (e.g., moving shocks) not contained in the span of the original reduced basis.
- Authors:
-
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1141744
- Report Number(s):
- SAND-2014-2732J
Journal ID: ISSN 0029-5981; 507023
- Grant/Contract Number:
- AC04-94AL85000
- Resource Type:
- Accepted Manuscript
- Journal Name:
- International Journal for Numerical Methods in Engineering
- Additional Journal Information:
- Journal Volume: 102; Journal Issue: 5; Journal ID: ISSN 0029-5981
- Publisher:
- Wiley
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; adaptive refinement; h-refinement; model reduction; dual-weighted residual; adjoint error estimation; clustering
Citation Formats
Carlberg, Kevin T. Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models. United States: N. p., 2014.
Web. doi:10.1002/nme.4800.
Carlberg, Kevin T. Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models. United States. https://doi.org/10.1002/nme.4800
Carlberg, Kevin T. Wed .
"Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models". United States. https://doi.org/10.1002/nme.4800. https://www.osti.gov/servlets/purl/1141744.
@article{osti_1141744,
title = {Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models},
author = {Carlberg, Kevin T.},
abstractNote = {Our work presents a method to adaptively refine reduced-order models a posteriori without requiring additional full-order-model solves. The technique is analogous to mesh-adaptive h-refinement: it enriches the reduced-basis space online by ‘splitting’ a given basis vector into several vectors with disjoint support. The splitting scheme is defined by a tree structure constructed offline via recursive k-means clustering of the state variables using snapshot data. This method identifies the vectors to split online using a dual-weighted-residual approach that aims to reduce error in an output quantity of interest. The resulting method generates a hierarchy of subspaces online without requiring large-scale operations or full-order-model solves. Furthermore, it enables the reduced-order model to satisfy any prescribed error tolerance regardless of its original fidelity, as a completely refined reduced-order model is mathematically equivalent to the original full-order model. Experiments on a parameterized inviscid Burgers equation highlight the ability of the method to capture phenomena (e.g., moving shocks) not contained in the span of the original reduced basis.},
doi = {10.1002/nme.4800},
journal = {International Journal for Numerical Methods in Engineering},
number = 5,
volume = 102,
place = {United States},
year = {Wed Nov 05 00:00:00 EST 2014},
month = {Wed Nov 05 00:00:00 EST 2014}
}
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