Results 11 to 20 of about 31,846 (223)
Polynomial Chaos Expansion for Operator Learning
arXiv.orgOperator learning (OL) has emerged as a powerful tool in scientific machine learning (SciML) for approximating mappings between infinite-dimensional functional spaces. One of its main applications is learning the solution operator of partial differential equations (PDEs).
Sharma, Himanshu +2 more
semanticscholar +4 more sources
Deep Polynomial Chaos Expansion
arXiv.orgPolynomial chaos expansion (PCE) is a classical and widely used surrogate modeling technique in physical simulation and uncertainty quantification. By taking a linear combination of a set of basis polynomials - orthonormal with respect to the distribution of uncertain input parameters - PCE enables tractable inference of key statistical quantities ...
Exenberger, Johannes +2 more
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On fractional moment estimation from polynomial chaos expansion
Reliability Engineering & System SafetyFractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by statistical sampling is challenging since it is typically not possible to create a large experimental design due to ...
Lukáš Novák +2 more
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Active Learning-based Domain Adaptive Localized Polynomial Chaos Expansion [PDF]
Mechanical systems and signal processing, 2023 The paper presents a novel methodology to build surrogate models of complicated functions by an active learning-based sequential decomposition of the input random space and construction of localized polynomial chaos expansions, referred to as domain ...
Lukáš Novák +3 more
semanticscholar +1 more source
Multivariate sensitivity-adaptive polynomial chaos expansion for high-dimensional surrogate modeling and uncertainty quantification [PDF]
Applied Mathematical Modelling, 2023 This work develops a novel basis-adaptive method for constructing anisotropic polynomial chaos expansions of multidimensional (vector-valued, multi-output) model responses.
Dimitrios Loukrezis +2 more
semanticscholar +1 more source
Probabilistic load margin assessment considering forecast error of wind power generation
Energy Reports, 2023 The increasing integration of wind power in power systems necessitates the probabilistic assessment of various uncertain factors. In operational planning, modeling short-term scale uncertainties, i.e., wind power forecast errors, plays an important role.
Chenxu Wang +3 more
doaj +1 more source
Polynomial chaos Kalman filter for target tracking applications
IET Radar, Sonar & Navigation, 2023 In this paper, an approximate Gaussian state estimator is developed based on generalised polynomial chaos expansion for target tracking applications. Motivated by the fact that calculating conditional moments in an approximate Gaussian filter involves ...
Kundan Kumar +3 more
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Frontiers in Physics, 2023 An efficient method of moments (MoM) based on polynomial chaos expansion (PCE) is applied to quickly calculate the electromagnetic scattering problems. The triangle basic functions are used to discretize the surface integral equations.
Xiaohui Yuan +5 more
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Projection Pursuit Adaptation on Polynomial Chaos Expansions
Computer Methods in Applied Mechanics and Engineering, 2022 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
Xiaoshu Zeng, Roger Ghanem
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A fully Bayesian sparse polynomial chaos expansion approach with joint priors on the coefficients and global selection of terms [PDF]
Journal of Computational Physics, 2022 Polynomial chaos expansion (PCE) is a versatile tool widely used in uncertainty quantification and machine learning, but its successful application depends strongly on the accuracy and reliability of the resulting PCE-based response surface.
P. Bürkner +3 more
semanticscholar +1 more source