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

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.
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0029-5981; 507023
Grant/Contract Number:
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
Research Org:
Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; 42 ENGINEERING adaptive refinement; h-refinement; model reduction; dual-weighted residual; adjoint error estimation; clustering