skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold

Authors:
ORCiD logo;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1638520
Resource Type:
Publisher's Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Volume: 370 Journal Issue: C; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Country of Publication:
Netherlands
Language:
English

Citation Formats

Giovanis, D. G., and Shields, M. D. Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold. Netherlands: N. p., 2020. Web. https://doi.org/10.1016/j.cma.2020.113269.
Giovanis, D. G., & Shields, M. D. Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold. Netherlands. https://doi.org/10.1016/j.cma.2020.113269
Giovanis, D. G., and Shields, M. D. Thu . "Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold". Netherlands. https://doi.org/10.1016/j.cma.2020.113269.
@article{osti_1638520,
title = {Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold},
author = {Giovanis, D. G. and Shields, M. D.},
abstractNote = {},
doi = {10.1016/j.cma.2020.113269},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 370,
place = {Netherlands},
year = {2020},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.cma.2020.113269

Save / Share:

Works referenced in this record:

Probabilistic learning for modeling and quantifying model-form uncertainties in nonlinear computational mechanics: PROBABILISTIC LEARNING FOR MODEL-FORM UNCERTAINTIES
journal, November 2018

  • Soize, C.; Farhat, C.
  • International Journal for Numerical Methods in Engineering, Vol. 117, Issue 7
  • DOI: 10.1002/nme.5980

Normalized cuts and image segmentation
journal, January 2000

  • Jianbo Shi, ; Malik, J.
  • IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 22, Issue 8
  • DOI: 10.1109/34.868688

Accelerated scale bridging with sparsely approximated Gaussian learning
journal, February 2020


The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
journal, November 2008

  • Foo, Jasmine; Wan, Xiaoliang; Karniadakis, George Em
  • Journal of Computational Physics, Vol. 227, Issue 22
  • DOI: 10.1016/j.jcp.2008.07.009

A Global Geometric Framework for Nonlinear Dimensionality Reduction
journal, December 2000


Nonequilibrium thermodynamics of driven amorphous materials. I. Internal degrees of freedom and volume deformation
journal, September 2009


Diffusion maps
journal, July 2006

  • Coifman, Ronald R.; Lafon, Stéphane
  • Applied and Computational Harmonic Analysis, Vol. 21, Issue 1
  • DOI: 10.1016/j.acha.2006.04.006

An Online Method for Interpolating Linear Parametric Reduced-Order Models
journal, January 2011

  • Amsallem, David; Farhat, Charbel
  • SIAM Journal on Scientific Computing, Vol. 33, Issue 5
  • DOI: 10.1137/100813051

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
journal, February 2019


Bayesian identification of a projection-based reduced order model for computational fluid dynamics
journal, April 2020


Polynomial-Chaos-Based Kriging
journal, January 2015


Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space
journal, January 2008

  • Bui-Thanh, T.; Willcox, K.; Ghattas, O.
  • SIAM Journal on Scientific Computing, Vol. 30, Issue 6
  • DOI: 10.1137/070694855

PLS-based adaptation for efficient PCE representation in high dimensions
journal, June 2019


Modeling and Quantification of Model-Form Uncertainties in Eigenvalue Computations Using a Stochastic Reduced Model
journal, March 2018

  • Farhat, Charbel; Bos, Adrien; Avery, Philip
  • AIAA Journal, Vol. 56, Issue 3
  • DOI: 10.2514/1.J056314

High-Order Collocation Methods for Differential Equations with Random Inputs
journal, January 2005

  • Xiu, Dongbin; Hesthaven, Jan S.
  • SIAM Journal on Scientific Computing, Vol. 27, Issue 3
  • DOI: 10.1137/040615201

Uncertainty Quantification in Multiscale Simulation of Materials: A Prospective
journal, July 2013


Nonlinear Component Analysis as a Kernel Eigenvalue Problem
journal, July 1998

  • Schölkopf, Bernhard; Smola, Alexander; Müller, Klaus-Robert
  • Neural Computation, Vol. 10, Issue 5
  • DOI: 10.1162/089976698300017467

Dynamical Properties of Truncated Wiener-Hermite Expansions
journal, January 1967


Adaptive sparse polynomial chaos expansion based on least angle regression
journal, March 2011


Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
journal, January 2006

  • Wan, Xiaoliang; Karniadakis, George Em
  • SIAM Journal on Scientific Computing, Vol. 28, Issue 3
  • DOI: 10.1137/050627630

Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
journal, April 2003

  • Donoho, D. L.; Grimes, C.
  • Proceedings of the National Academy of Sciences, Vol. 100, Issue 10
  • DOI: 10.1073/pnas.1031596100

Modeling uncertainties in molecular dynamics simulations using a stochastic reduced-order basis
journal, September 2019

  • Wang, Haoran; Guilleminot, Johann; Soize, Christian
  • Computer Methods in Applied Mechanics and Engineering, Vol. 354
  • DOI: 10.1016/j.cma.2019.05.020

Nonlinear Dimensionality Reduction by Locally Linear Embedding
journal, December 2000


Dynamics of viscoplastic deformation in amorphous solids
journal, June 1998


A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
journal, January 2015

  • Benner, Peter; Gugercin, Serkan; Willcox, Karen
  • SIAM Review, Vol. 57, Issue 4
  • DOI: 10.1137/130932715

Deformation and Failure of Amorphous, Solidlike Materials
journal, March 2011


Evaluation of the Disorder Temperature and Free-Volume Formalisms via Simulations of Shear Banding in Amorphous Solids
journal, May 2007


Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
journal, January 2004


Uncertainty quantification for complex systems with very high dimensional response using Grassmann manifold variations
journal, July 2018


Riemannian center of mass and mollifier smoothing
journal, September 1977


An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations
journal, May 2009


Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity
journal, July 2008

  • Amsallem, David; Farhat, Charbel
  • AIAA Journal, Vol. 46, Issue 7
  • DOI: 10.2514/1.35374

Coarse graining atomistic simulations of plastically deforming amorphous solids
journal, May 2017


Data-driven probability concentration and sampling on manifold
journal, September 2016


Sparse On-Line Gaussian Processes
journal, March 2002


AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation
journal, March 2011


The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
journal, January 2002


Assessing the Performance of leja and Clenshaw-Curtis Collocation for Computational Electromagnetics with Random Input data
journal, January 2019


Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
journal, June 2003


Variance‐based simplex stochastic collocation with model order reduction for high‐dimensional systems
journal, November 2018

  • Giovanis, D. G.; Shields, M. D.
  • International Journal for Numerical Methods in Engineering, Vol. 117, Issue 11
  • DOI: 10.1002/nme.5992

Schubert Varieties and Distances between Subspaces of Different Dimensions
journal, January 2016

  • Ye, Ke; Lim, Lek-Heng
  • SIAM Journal on Matrix Analysis and Applications, Vol. 37, Issue 3
  • DOI: 10.1137/15M1054201

An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
journal, November 2005


A tutorial on spectral clustering
journal, August 2007


A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
journal, January 2007

  • Babuška, Ivo; Nobile, Fabio; Tempone, Raúl
  • SIAM Journal on Numerical Analysis, Vol. 45, Issue 3
  • DOI: 10.1137/050645142

Extending Classical Surrogate Modeling to high Dimensions Through Supervised Dimensionality Reduction: a Data-Driven Approach
journal, January 2020


Parallel three-dimensional simulations of quasi-static elastoplastic solids
journal, March 2020


The Geometry of Algorithms with Orthogonality Constraints
journal, January 1998

  • Edelman, Alan; Arias, Tomás A.; Smith, Steven T.
  • SIAM Journal on Matrix Analysis and Applications, Vol. 20, Issue 2
  • DOI: 10.1137/S0895479895290954

Riemannian Geometry of Grassmann Manifolds with a View on Algorithmic Computation
journal, January 2004


An adaptive local reduced basis method for solving PDEs with uncertain inputs and evaluating risk
journal, March 2019

  • Zou, Zilong; Kouri, Drew; Aquino, Wilkins
  • Computer Methods in Applied Mechanics and Engineering, Vol. 345
  • DOI: 10.1016/j.cma.2018.10.028