Recent Advances in Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Analysis and Design

By Michael S. Eldred. 2009

380 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/aa7f35cc6a1b6f518b4cf1885f7390f2e6b4c558

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In Civil and Structural Engineering

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Citations in the corpus

Polynomial-Chaos-based Kriging (2015, methodology): “Further recent applications of PCE to structural reliability analysis and design optimization can be found in Eldred (2009); Eldred et al. (2008); Sarangi et al. (2014).”
A Stochastic Collocation Algorithm with Multifidelity Models (2014, background): “From the applied mathematics community, one standard technique involves corrections where the difference between the low- and high-fidelity models is approximated by a surrogate [14, 14, 9, 17].”
First order reliability method for time-variant problems using series expansions (2015, methodology): “After a surrogate model for Gmax is established (Žilinskas 1992; Wang et al. 2001; Eldred and Burkardt 2009; Sudret 2008; Eldred 2009; Richard et al. 2012), the time-variant problem is then transformed into a timeinvariant problem.”
Silicon Photonics Circuit Design: Methods, Tools and Challenges (2018, methodology): “In polynomial chaos expansion (PCE), the system model is replaced with a higher-order model where the distribution of the low-level parameters is directly mapped onto the distribution of the performance metrics of the system [136, 137].”
Review of multi-fidelity models (2016, methodology): “PCE has been applied in the context of MFM in several studies, such as Eldred (2009) [58], Ng and Eldred (2012) [159], Padr´on et al. (2014) [164], Padr´on et al. (2016) [163] and Absi and Mahadevan (2016) [1].”
A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems (2019, methodology): “Several methods have been developed to estimate such correlations, such as the response surface models [11, 12], polynomial chaos expansion [13, 14], Gaussian process regression (GPR) [6, 8, 9, 15], artiﬁcial neural networks [16], and moving least squares [17, 18].”
A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing (2011, methodology): “, [31,33]), and response surface approximation methods (e.”