Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics

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Least squares polynomial chaos expansion: A review of sampling strategies (2017, methodology): “The main task in PC-based methods is to compute the PC coefficients either intrusively or non-intrusively [40, 72].”
Model order reduction based on proper generalized decomposition for the propagation of uncertainties in structural dynamics (2012, unknown): “This parametric vision, combined with approximation theory and numerical analysis, brought to the so-called spectral stochastic methods [10, 33, 18, 23, 36, 16].”
An introduction to sampling via measure transport (2016, background): “The resulting map can then be viewed as a polynomial chaos expansion [94, 46] of a random variable distributed according to the target measure.”
Quantification of model uncertainty in RANS simulations: A review (2018, methodology): “They used Karhunen–Loeve (KL) expansions [71] to approximately represent the perturbation field with leading modes in KL expansion (see Equation (39)).”
Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data (2019, methodology): “Because of the non-intrusive feature and ease of implementation, data-ﬁt surrogates have been used for a wide range of forward and inverse uncertainty quantiﬁcation (UQ) problems in ﬂuid dynamics [14, 16, 17].”