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On-the-Fly Bayesian Data Assimilation Using Transport Map Sampling and PGD Reduced Models

  • Paul-Baptiste Rubio
  • Ludovic ChamoinEmail author
  • François Louf
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Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 93)

Abstract

The motivation of this research work is to address real-time sequential data assimilation and inference of model parameters within a full Bayesian formulation. For that purpose, we couple two advanced numerical approaches. First, the Transport Map sampling is used as an alternative to classical Markov Chain approaches in order to facilitate the sampling of posterior densities resulting from Bayesian inference. It builds a deterministic mapping, obtained from a minimization problem, between the posterior probability measure of interest and a simple reference measure. Second, the Proper Generalized Decomposition (PGD) is implemented in order to reduce the computational effort for the evaluation of the multi-parametric numerical model in the online phase, and therefore for uncertainty quantification on outputs of interest of the model. The PGD also speeds up the minimization algorithm of the Transport Map method, as derivatives with respect to model parameters can then be computed in a straightforward manner. The performance of the approach is illustrated on a fusion welding application.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Paul-Baptiste Rubio
    • 1
  • Ludovic Chamoin
    • 1
    Email author
  • François Louf
    • 1
  1. 1.LMT ENS Paris-SaclayCachanFrance

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