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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
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Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques.

Andrea Zanoni1, Gianluca Geraci2, Matteo Salvador1

  • 1Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA.

Computer Methods in Applied Mechanics and Engineering
|June 24, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces new multifidelity Monte Carlo estimators for computationally expensive models. These methods reduce uncertainty by creating a shared parameter subspace, improving accuracy and efficiency.

Keywords:
Monte Carlo estimatorsactive subspacesautoencodersmultifidelitynormalizing flowsuncertainty quantification

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Area of Science:

  • Computational Science
  • Uncertainty Quantification
  • Numerical Analysis

Background:

  • Multifidelity uncertainty propagation is crucial for expensive computational models.
  • Existing methods struggle with dissimilar parameterizations between high-fidelity and low-fidelity models.

Purpose of the Study:

  • To develop novel multifidelity Monte Carlo estimators for general settings.
  • To address challenges posed by differing parameterizations and probability distributions.

Main Methods:

  • Derivation of multifidelity Monte Carlo estimators utilizing a shared Gaussian subspace.
  • Employing normalizing flows for probability distribution mapping.
  • Utilizing active subspaces and autoencoders for dimensionality reduction.

Main Results:

  • Constructed modified low-fidelity models with increased correlation to high-fidelity models.
  • Achieved reduced variance in multifidelity estimators.
  • Demonstrated advantages through numerical experiments.

Conclusions:

  • The proposed methods effectively handle dissimilar model parameterizations.
  • The novel estimators offer significant improvements in uncertainty propagation accuracy and efficiency.