Model Adaptivity for Goal-Oriented Inference using Adjoints
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Author(s)
Li, Harriet
Garg, Vikram V.
Willcox, Karen E
Alternative Title
Model adaptivity for goal-oriented inference using adjoints
Date Issued
November 2017
Journal
Computer Methods in Applied Mechanics and Engineering
Publisher
Elsevier BV
Citation
Li, Harriet, Vikram V. Garg, and Karen Willcox. "Model adaptivity for goal-oriented inference using adjoints." Computer Methods in Applied Mechanics and Engineering, 331 (April 2018): 1-22.
Version
Author's final manuscript
Abstract
An inverse problem seeks to infer unknown model parameters using observed data. We consider a goal-oriented inverse problem, where the goal of inferring parameters is to use them in predicting a quantity of interest (QoI). Recognizing that multiple models of varying fidelity and computational cost may be available to describe the physical system, we formulate a goal-oriented model adaptivity approach that leverages multiple models while controlling the error in the QoI prediction. In particular, we adaptively form a mixed-fidelity model by using models of different levels of fidelity in different subregions of the domain. Taking the solution of the inverse problem with the highest-fidelity model as our reference QoI prediction, we derive an adjoint-based third-order estimate for the QoI error from using a lower-fidelity model. Localization of this error then guides the formation of mixed-fidelity models. We demonstrate the method for example problems described by convection–diffusion–reaction models. For these examples, our mixed-fidelity models use the high-fidelity model over only a small portion of the domain, but result in QoI estimates with small relative errors. We also demonstrate that the mixed-fidelity inverse problems can be cheaper to solve and less sensitive to the initial guess than the high-fidelity inverse problems. Keyword: Inference; Goal-oriented adaptive modeling; A posteriori error estimation; Multi-fidelity modeling; Adjoints
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.cma.2017.11.018
