Projection pursuit adaptation on polynomial chaos expansions

DOI10.1016/j.cma.2022.115845OpenAlexW4312109041MaRDI QIDQ2683425

X. Zeng, Roger G. Ghanem

Publication date: 10 February 2023

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.13420

zbMATH Keywords

dimension reductionprojection pursuithigh-dimensional modelspolynomial chaos expansiondata-drivensurrogate modeling

Mathematics Subject Classification ID

Statistics (62-XX) Numerical analysis (65-XX)

Related Items (2)

Multifidelity uncertainty quantification with models based on dissimilar parameters ⋮ Surrogate-accelerated Bayesian framework for high-temperature thermal diffusivity characterization

Uses Software

• ElemStatLearn
• PMTK
• UMAP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Basis adaptation in homogeneous chaos spaces
• Compressive sampling of polynomial chaos expansions: convergence analysis and sampling strategies
• Multi-output local Gaussian process regression: applications to uncertainty quantification
• Uncertainty quantification. An accelerated course with advanced applications in computational engineering
• A non-adapted sparse approximation of PDEs with stochastic inputs
• Adaptive sparse polynomial chaos expansion based on least angle regression
• Stochastic spectral methods for efficient Bayesian solution of inverse problems
• Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach
• Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
• Projection pursuit
• Numerical integration using sparse grids
• Reduced Wiener chaos representation of random fields via basis adaptation and projection
• Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos
• Simple cubature formulas with high polynomial exactness
• Ingredients for a general purpose stochastic finite elements implementation
• Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold
• B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
• Probabilistic learning on manifolds constrained by nonlinear partial differential equations for small datasets
• Stochastic modeling of geometrical uncertainties on complex domains, with application to additive manufacturing and brain interface geometries
• Bayesian neural networks for uncertainty quantification in data-driven materials modeling
• Accelerated basis adaptation in homogeneous chaos spaces
• Functional projection pursuit regression
• Active Subspaces
• Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs
• Bayesian Design and Analysis of Computer Experiments: Use of Derivatives in Surface Prediction
• Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics
• Spectral Methods for Uncertainty Quantification
• Exploratory Projection Pursuit
• Gaussian Hilbert Spaces
• A Projection Pursuit Algorithm for Exploratory Data Analysis
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Optimal weighted least-squares methods
• DIMENSIONALITY REDUCTION FOR COMPLEX MODELS VIA BAYESIAN COMPRESSIVE SENSING
• Addressing the curse of dimensionality in stochastic dynamics: a Wiener path integral variational formulation with free boundaries
• Remarks on a Multivariate Transformation
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
• Stochastic Dynamics of Structures

This page was built for publication: Projection pursuit adaptation on polynomial chaos expansions