Projection pursuit adaptation on polynomial chaos expansions

Zeng, Xiaoshu; Ghanem, Roger

doi:10.1016/j.cma.2022.115845

Projection pursuit adaptation on polynomial chaos expansions

Journal Article · Wed Dec 20 23:00:00 EST 2023 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2022.115845· OSTI ID:2421877

^[1]; ^[2]

Univ. of Southern California, Los Angeles, CA (United States); OSTI
Univ. of Southern California, Los Angeles, CA (United States)

Here, the present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos expansions (PCE) were recently proposed to construct low-dimensional approximations adapted to specific quantities of interest (QoI). The present paper addresses one difficulty with these adaptations, namely their reliance on quadrature point sampling, which limits the reusability of potentially expensive samples. Projection pursuit (PP) is a statistical tool to find the “interesting” projections in high-dimensional data and thus bypass the curse-of-dimensionality. In the present work, we combine the fundamental ideas of basis adaptation and projection pursuit regression (PPR) to propose a novel method to simultaneously learn the optimal low-dimensional spaces and PCE representation from given data. While this projection pursuit adaptation (PPA) can be entirely data-driven, the constructed approximation exhibits mean-square convergence to the solution of an underlying governing equation and thus captures the supports and probability distributions associated with the physics constraints. The proposed approach is demonstrated on a borehole problem and a structural dynamics problem, demonstrating the versatility of the method and its ability to discover low-dimensional manifolds with high accuracy with limited data. In addition, the method can learn surrogate models for different quantities of interest while reusing the same data set.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Southern California, Los Angeles, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); US Department of the Navy, Office of Naval Research (ONR)

Grant/Contract Number:: SC0021307

OSTI ID:: 2421877

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: C Vol. 405; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (51)

Serviceability-based damping optimization of randomly wind-excited high-rise buildings Zeng, Xiaoshu; Peng, Yongbo; Chen, Jianbing The Structural Design of Tall and Special Buildings, Vol. 26, Issue 11 https://doi.org/10.1002/tal.1371	journal	April 2017
Application of projection pursuit regression to thermal error modeling of a CNC machine tool Qianjian, Guo; Jianguo, Yang The International Journal of Advanced Manufacturing Technology, Vol. 55, Issue 5-8 https://doi.org/10.1007/s00170-010-3114-4	journal	December 2010
Simple Cubature Formulas with High Polynomial Exactness Novak, Erich; Ritter, Klaus Constructive Approximation, Vol. 15, Issue 4 https://doi.org/10.1007/s003659900119	journal	October 1999
Functional projection pursuit regression Ferraty, F.; Goia, A.; Salinelli, E. TEST, Vol. 22, Issue 2 https://doi.org/10.1007/s11749-012-0306-2	journal	August 2012
Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos Xiu, Dongbin; Em Karniadakis, George Computer Methods in Applied Mechanics and Engineering, Vol. 191, Issue 43 https://doi.org/10.1016/S0045-7825(02)00421-8	journal	September 2002
Ingredients for a general purpose stochastic finite elements implementation Ghanem, Roger Computer Methods in Applied Mechanics and Engineering, Vol. 168, Issue 1-4 https://doi.org/10.1016/S0045-7825(98)00106-6	journal	January 1999
Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach Ghanem, Roger; Red-Horse, John Physica D: Nonlinear Phenomena, Vol. 133, Issue 1-4 https://doi.org/10.1016/S0167-2789(99)00102-5	journal	September 1999
Supervised projection pursuit – A dimensionality reduction technique optimized for probabilistic classification Barcaru, Andrei Chemometrics and Intelligent Laboratory Systems, Vol. 194 https://doi.org/10.1016/j.chemolab.2019.103867	journal	November 2019
Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold Giovanis, D. G.; Shields, M. D. Computer Methods in Applied Mechanics and Engineering, Vol. 370 https://doi.org/10.1016/j.cma.2020.113269	journal	October 2020
Probabilistic learning on manifolds constrained by nonlinear partial differential equations for small datasets Soize, C.; Ghanem, R. Computer Methods in Applied Mechanics and Engineering, Vol. 380 https://doi.org/10.1016/j.cma.2021.113777	journal	July 2021
Stochastic modeling of geometrical uncertainties on complex domains, with application to additive manufacturing and brain interface geometries Zhang, Hao; Guilleminot, Johann; Gomez, Luis J. Computer Methods in Applied Mechanics and Engineering, Vol. 385 https://doi.org/10.1016/j.cma.2021.114014	journal	November 2021
Bayesian neural networks for uncertainty quantification in data-driven materials modeling Olivier, Audrey; Shields, Michael D.; Graham-Brady, Lori Computer Methods in Applied Mechanics and Engineering, Vol. 386 https://doi.org/10.1016/j.cma.2021.114079	journal	December 2021
Accelerated basis adaptation in homogeneous chaos spaces Zeng, Xiaoshu; Red-Horse, John; Ghanem, Roger Computer Methods in Applied Mechanics and Engineering, Vol. 386 https://doi.org/10.1016/j.cma.2021.114109	journal	December 2021
Integrated stochastic analysis of fiber composites manufacturing using adapted polynomial chaos expansions Ghauch, Ziad G.; Aitharaju, Venkat; Rodgers, William R. Composites Part A: Applied Science and Manufacturing, Vol. 118 https://doi.org/10.1016/j.compositesa.2018.12.029	journal	March 2019
Stochastic spectral methods for efficient Bayesian solution of inverse problems Marzouk, Youssef M.; Najm, Habib N.; Rahn, Larry A. Journal of Computational Physics, Vol. 224, Issue 2 https://doi.org/10.1016/j.jcp.2006.10.010	journal	June 2007
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems Marzouk, Youssef M.; Najm, Habib N. Journal of Computational Physics, Vol. 228, Issue 6 https://doi.org/10.1016/j.jcp.2008.11.024	journal	April 2009
Adaptive sparse polynomial chaos expansion based on least angle regression Blatman, Géraud; Sudret, Bruno Journal of Computational Physics, Vol. 230, Issue 6 https://doi.org/10.1016/j.jcp.2010.12.021	journal	March 2011
A non-adapted sparse approximation of PDEs with stochastic inputs Doostan, Alireza; Owhadi, Houman Journal of Computational Physics, Vol. 230, Issue 8 https://doi.org/10.1016/j.jcp.2011.01.002	journal	April 2011
Multi-output local Gaussian process regression: Applications to uncertainty quantification Bilionis, Ilias; Zabaras, Nicholas Journal of Computational Physics, Vol. 231, Issue 17 https://doi.org/10.1016/j.jcp.2012.04.047	journal	July 2012
Basis adaptation in homogeneous chaos spaces Tipireddy, Ramakrishna; Ghanem, Roger Journal of Computational Physics, Vol. 259 https://doi.org/10.1016/j.jcp.2013.12.009	journal	February 2014
Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies Hampton, Jerrad; Doostan, Alireza Journal of Computational Physics, Vol. 280 https://doi.org/10.1016/j.jcp.2014.09.019	journal	January 2015
Reduced Wiener Chaos representation of random fields via basis adaptation and projection Tsilifis, Panagiotis; Ghanem, Roger G. Journal of Computational Physics, Vol. 341 https://doi.org/10.1016/j.jcp.2017.04.009	journal	July 2017
B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data Yang, Liu; Meng, Xuhui; Karniadakis, George Em Journal of Computational Physics, Vol. 425 https://doi.org/10.1016/j.jcp.2020.109913	journal	January 2021
Assessment of phytotoxicity grade during composting based on EEM/PARAFAC combined with projection pursuit regression Cui, Hong-Yang; Zhao, Yue; Chen, Yan-Ni Journal of Hazardous Materials, Vol. 326 https://doi.org/10.1016/j.jhazmat.2016.09.059	journal	March 2017
Probabilistic analysis of wind-induced vibration mitigation of structures by fluid viscous dampers Chen, Jianbing; Zeng, Xiaoshu; Peng, Yongbo Journal of Sound and Vibration, Vol. 409 https://doi.org/10.1016/j.jsv.2017.07.051	journal	November 2017
Feature selection in machine learning: A new perspective Cai, Jie; Luo, Jiawei; Wang, Shulin Neurocomputing, Vol. 300 https://doi.org/10.1016/j.neucom.2017.11.077	journal	July 2018
An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis Blatman, Géraud; Sudret, Bruno Probabilistic Engineering Mechanics, Vol. 25, Issue 2 https://doi.org/10.1016/j.probengmech.2009.10.003	journal	April 2010
An analytical Wiener path integral technique for non-stationary response determination of nonlinear oscillators Kougioumtzoglou, I. A.; Spanos, P. D. Probabilistic Engineering Mechanics, Vol. 28 https://doi.org/10.1016/j.probengmech.2011.08.022	journal	April 2012
A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters Chen, Jianbing; Yang, Junyi; Li, Jie Structural Safety, Vol. 59 https://doi.org/10.1016/j.strusafe.2015.11.001	journal	March 2016
Wiener path integrals and multi-dimensional global bases for non-stationary stochastic response determination of structural systems Psaros, Apostolos F.; Petromichelakis, Ioannis; Kougioumtzoglou, Ioannis A. Mechanical Systems and Signal Processing, Vol. 128 https://doi.org/10.1016/j.ymssp.2019.04.014	journal	August 2019
Homogeneous chaos basis adaptation for design optimization under uncertainty: Application to the oil well placement problem Thimmisetty, Charanraj; Tsilifis, Panagiotis; Ghanem, Roger Artificial Intelligence for Engineering Design, Analysis and Manufacturing, Vol. 31, Issue 3 https://doi.org/10.1017/S0890060417000166	journal	August 2017
Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs Schwab, Christoph; Gittelson, Claude Jeffrey Acta Numerica, Vol. 20 https://doi.org/10.1017/S0962492911000055	journal	April 2011
Leveraging uncertainty information from deep neural networks for disease detection Leibig, Christian; Allken, Vaneeda; Ayhan, Murat Seçkin Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-017-17876-z	journal	December 2017
Molecular function recognition by supervised projection pursuit machine learning Grear, Tyler; Avery, Chris; Patterson, John Scientific Reports, Vol. 11, Issue 1 https://doi.org/10.1038/s41598-021-83269-y	journal	February 2021
Bayesian Design and Analysis of Computer Experiments: Use of Derivatives in Surface Prediction Morris, Max D.; Mitchell, Toby J.; Ylvisaker, Donald Technometrics, Vol. 35, Issue 3 https://doi.org/10.1080/00401706.1993.10485320	journal	August 1993
Gaussian Process Single-Index Models as Emulators for Computer Experiments Gramacy, Robert B.; Lian, Heng Technometrics, Vol. 54, Issue 1 https://doi.org/10.1080/00401706.2012.650527	journal	February 2012
Projection Pursuit Regression Friedman, Jerome H.; Stuetzle, Werner Journal of the American Statistical Association, Vol. 76, Issue 376 https://doi.org/10.1080/01621459.1981.10477729	journal	December 1981
Exploratory Projection Pursuit Friedman, Jerome H. Journal of the American Statistical Association, Vol. 82, Issue 397 https://doi.org/10.1080/01621459.1987.10478427	journal	March 1987
Analysis of Dimensionality Reduction Techniques on Big Data Reddy, G. Thippa; Reddy, M. Praveen Kumar; Lakshmanna, Kuruva IEEE Access, Vol. 8 https://doi.org/10.1109/ACCESS.2020.2980942	journal	January 2020
A Projection Pursuit Algorithm for Exploratory Data Analysis Friedman, J. H.; Tukey, J. W. IEEE Transactions on Computers, Vol. C-23, Issue 9 https://doi.org/10.1109/T-C.1974.224051	journal	September 1974
Riemannian Manifold Learning No authors listed IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 30, Issue 5 https://doi.org/10.1109/TPAMI.2007.70735	journal	May 2008
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data Babuška, Ivo; Nobile, Fabio; Tempone, Raúl SIAM Journal on Numerical Analysis, Vol. 45, Issue 3 https://doi.org/10.1137/050645142	journal	January 2007
Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces Constantine, Paul G.; Dow, Eric; Wang, Qiqi SIAM Journal on Scientific Computing, Vol. 36, Issue 4 https://doi.org/10.1137/130916138	journal	January 2014
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations Xiu, Dongbin; Karniadakis, George Em SIAM Journal on Scientific Computing, Vol. 24, Issue 2 https://doi.org/10.1137/S1064827501387826	journal	January 2002
Gaussian Processes for Machine Learning Seeger, Matthias International Journal of Neural Systems, Vol. 14, Issue 02 https://doi.org/10.1142/S0129065704001899	journal	April 2004
Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics Najm, Habib N. Annual Review of Fluid Mechanics, Vol. 41, Issue 1 https://doi.org/10.1146/annurev.fluid.010908.165248	journal	January 2009
A Nonlinear Approach to Regional Flood Frequency Analysis Using Projection Pursuit Regression Durocher, Martin; Chebana, Fateh; Ouarda, Taha B. M. J. Journal of Hydrometeorology, Vol. 16, Issue 4 https://doi.org/10.1175/JHM-D-14-0227.1	journal	July 2015
Projection Pursuit for Exploratory Supervised Classification Lee, Eun-Kyung; Cook, Dianne; Klinke, Sigbert Journal of Computational and Graphical Statistics, Vol. 14, Issue 4 https://doi.org/10.1198/106186005X77702	journal	December 2005
Remarks on a Multivariate Transformation Rosenblatt, Murray The Annals of Mathematical Statistics, Vol. 23, Issue 3 https://doi.org/10.1214/aoms/1177729394	journal	September 1952
Dimensionality Reduction for Complex Models via Bayesian Compressive Sensing Sargsyan, Khachik; Safta, Cosmin; Najm, Habib N. International Journal for Uncertainty Quantification, Vol. 4, Issue 1 https://doi.org/10.1615/Int.J.UncertaintyQuantification.2013006821	journal	January 2014
Optimal weighted least-squares methods Cohen, Albert; Migliorati, Giovanni The SMAI journal of computational mathematics, Vol. 3 https://doi.org/10.5802/smai-jcm.24	journal	October 2017

Similar Records

A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems

Journal Article · Mon May 23 00:00:00 EDT 2022 · Journal of Computational Physics · OSTI ID:1906444

Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis

Journal Article · Fri Feb 28 23:00:00 EST 2014 · Journal of Computational Physics · OSTI ID:22230875

Related Subjects

97 MATHEMATICS AND COMPUTING
Data-driven
Dimension reduction
Engineering
High-dimensional models
Mathematics
Mechanics
Polynomial chaos expansion
Projection pursuit
Surrogate modeling

Projection pursuit adaptation on polynomial chaos expansions

Citation Formats

References (51)

Similar Records

Related Subjects