Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics

By Habib N. Najm. 2009

824 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1ef8d786a16ad94238ca26fb008a350bf7245047

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Citations in the corpus

Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data (2019, background): “Namely, a deterministic or probabilistic input-output mapping is constructed using, e.g., polynomial basis functions [9], radial basis functions [10], Gaussian process (GP) [11, 12], and stochastic polynomial chaos expansion (PCE) [13–15], among others.”
Design-space dimensionality reduction in shape optimization by Karhunen–Loève expansion (2015, background): “In a Bayesian approach, f represents the degree of belief in a proposition [28] and may be selected according to the designer’s experience.”
Simulation-based optimal Bayesian experimental design for nonlinear systems (2011, background): “Many options exist, ranging from projection-based model reduction [45, 46] to spectral methods based on polynomial chaos (PC) expansions [47, 22, 23, 48, 49, 50, 51].”
A review of uncertainty analysis in building energy assessment (2018, methodology): “The advantage of internal (non-sampling) methods is their ability to provide high accuracy and high efficiency results, while this method requires extensively modifying the existing computational system code for uncertainty propagation [106].”
Nonlinear Propagation of Orbit Uncertainty Using Non-Intrusive Polynomial Chaos (2013, methodology): “Although not yet applied in astrodynamics, previous research using PC includes uncertainty quantification in engineering fields such as: fluid dynamics [11–18], solid mechanics [19–22], multibody dynamics [23,24], high-order state estimation [25,26], and many other applications.”
Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks (2019, methodology): “Traditional choices for surrogate models include Gaussian process regression (GPR) (or Kriging) [15, 16, 17, 18, 19], polynomial chaos expansion [20, 21, 22, 23], and radial basis functions [24, 25].”
Adversarial Uncertainty Quantification in Physics-Informed Neural Networks (2018, background): “However, despite the fact that much progress has been made over the last two decades, the most popular methods for scientific computing under uncertainty, such as polynomial chaos expansions [17, 18, 19], sparse grid quadratures [20, 21], multi-level/multi-fidelity Monte Carlo sampling [22, 23], pro”