Multi-output Local Gaussian Process Regression: Applications to Uncertainty Quantification

Abstract

We develop an efficient, Bayesian Uncertainty Quantification framework us- ing a novel treed Gaussian process model. The tree is adaptively constructed using information conveyed by the observed data about the length scales of the underlying process. On each leaf of the tree, we utilize Bayesian Experimental Design techniques in order to learn a multi-output Gaussian process. The constructed surrogate can provide analytical point estimates, as well as error bars, for the statistics of interest. We numerically demonstrate the effectiveness of the suggested framework in identifying discontinuities, local features and unimportant dimensions in the solution of stochastic differential equations.

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Document Details

Document Type
Technical Report
Publication Date
Dec 07, 2011
Accession Number
ADA554929

Entities

People

  • Ilias Bilionis
  • Nicholas Zabaras

Organizations

  • Cornell University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Bayesian Networks
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Programs
  • Data Science
  • Differential Equations
  • Equations
  • Gaussian Processes
  • Information Science
  • Partial Differential Equations
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistical Algorithms
  • Statistics
  • Two Dimensional

Fields of Study

  • Computer science

Readers

  • Computer Vision.
  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms