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

  • 2025
  • OriginalPaper
  • Chapter
Published in:
Authors
Alessandra Vizzaccaro
Mikkel B. Lykkegaard
Tim Dodwell
Published in
Data Science in Engineering Vol. 10
Publisher
Springer Nature Switzerland

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Abstract

This chapter delves into the integration of Markov Chain Monte Carlo (MCMC) techniques with matrix manifolds for probabilistic model order reduction. The primary focus is on linear model order reduction (MOR), which aims to minimize the dimensionality of problems while preserving essential patterns. The methodology involves searching for optimal matrices on matrix manifolds, such as the Stiefel and Grassmann manifolds, to solve various applications including proper orthogonal decomposition, active subspaces, and matrix completion. By adapting MCMC algorithms like Metropolis-Hastings and Metropolis-adjusted Langevin algorithm, the work enables drawing samples from posterior distributions defined on matrix manifolds, effectively quantifying uncertainty. The proposed framework, implemented using the Manopt software, offers a robust approach to propagating uncertainty in reduced models, making it a valuable contribution to the field of probabilistic MOR.
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The original version of the chapter has been revised. A correction to this chapter can be found at https://doi.org/10.1007/978-3-031-68142-4_18

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previous chapter On the Use of Symbolic Regression for Population-Based Modelling of Structures
next chapter Identification of Bird Species in Large Multi-channel Data Streams Using Distributed Acoustic Sensing
Title
Markov Chain Monte Carlo on Matrix Manifolds for Probabilistic Model Order Reduction
Authors
Alessandra Vizzaccaro
Mikkel B. Lykkegaard
Tim Dodwell
Copyright Year
2025
Book
Data Science in Engineering Vol. 10

Print ISBN: 978-3-031-68141-7

Electronic ISBN: 978-3-031-68142-4

Copyright Year: 2025

DOI
https://doi.org/10.1007/978-3-031-68142-4_12
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