Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models

Carlberg, Kevin T.

doi:10.1002/nme.4800

Title: 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:

Carlberg, Kevin T. ^[1]

Sandia National Lab. (SNL-CA), Livermore, CA (United States)

Publication Date:: Wed Nov 05 00:00:00 EST 2014

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:: Journal Article: 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.

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                    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

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                    Carlberg, Kevin T. 2014.  
        "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.

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@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},

  url          = {https://www.osti.gov/biblio/1141744},
  journal      = {International Journal for Numerical Methods in Engineering},

  issn         = {0029-5981},

  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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Title: Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models

Abstract

Citation Formats

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