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This work extends classical tools in linear model order reduction and more recent results in the field of optimization on Riemannian manifolds to the probabilistic case, within the Bayesian framework. We present a method to draw samples from a given target distribution defined on various matrix manifolds. The collected samples can be used to propagate uncertainty on the reduction matrix and other quantities of interest.

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Markov Chain Monte Carlo on Matrix Manifolds for Probabilistic Model Order Reduction

  • 会议论文

  • 发表日期：

    2025年

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  • Alessandra Vizzaccaro,
  • Mikkel B. Lykkegaard,
  • Tim Dodwell

摘要

This work extends classical tools in linear model order reduction and more recent results in the field of optimization on Riemannian manifolds to the probabilistic case, within the Bayesian framework. We present a method to draw samples from a given target distribution defined on various matrix manifolds. The collected samples can be used to propagate uncertainty on the reduction matrix and other quantities of interest.