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Basics of Multivariate Analysis in Neuroimaging Data
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Multi-fidelity modelling via recursive co-kriging and Gaussian-Markov random fields.

P Perdikaris1, D Venturi1, J O Royset2

  • 1Division of Applied Mathematics , Brown University , Providence, RI 02912, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|September 8, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a novel framework for design under uncertainty, blending multi-fidelity models and probability spaces using advanced machine learning. The approach enhances accuracy in complex system analysis and risk-averse design.

Keywords:
big datamachine learningresponse surfacesrisk-averse designsurrogate modellinguncertainty quantification

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Area of Science:

  • Computational Science
  • Engineering
  • Machine Learning

Background:

  • Design under uncertainty poses significant challenges in complex dynamical systems.
  • Integrating multi-fidelity models and probabilistic methods is crucial for accurate analysis.
  • Existing methods often struggle to efficiently blend diverse information sources.

Purpose of the Study:

  • To develop a unified framework for design under uncertainty.
  • To incorporate multi-fidelity models and multi-fidelity probability spaces.
  • To enable efficient and accurate response surface construction for complex systems.

Main Methods:

  • Stochastic computer simulations and multi-level recursive co-kriging.
  • Auto-regressive stochastic modeling for blending information sources.
  • Machine learning framework utilizing sparse precision matrices of Gaussian-Markov random fields.

Main Results:

  • Successful construction of response surfaces for complex dynamical systems.
  • Demonstrated effectiveness in risk-averse design problems.
  • Accurate uncertainty quantification in fluid mechanics simulations (e.g., Burgers equation, laminar wakes).

Conclusions:

  • The proposed framework offers a computationally efficient and effective approach to design under uncertainty.
  • The methodology successfully integrates multi-fidelity data for improved predictive modeling.
  • This work advances the state-of-the-art in uncertainty quantification and risk-averse design.