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

2010

634 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f94b22fd1c4b1fad8e4efd6621fce2e1cca46e5c

Citations in the corpus

• Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier-Stokes simulations: A data-driven, physics-informed Bayesian approach (2015, unknown): “(3) for the fields δ, δ and δ become Karhunen–Loeve (KL) expansions [31], such that ω i , ω ξ i , and ω η i are uncorrelated random variables with zero means and unit variances.”
• 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”
• Approximation of high-dimensional parametric PDEs * (2015, result): “We refer in particular to [40, 46, 55, 56, 90] for general introductions to these approaches, and to [1, 41, 37, 53, 54, 83, 84] for related work prior to the results exposed in our paper.”
• Bayesian updating via bootstrap filtering combined with data-driven polynomial chaos expansions: methodology and application to history matching for carbon dioxide storage in geological formations (2013, background): “, in the form of high-order statistical moments) [26, 37, 88], which goes beyond the scope of the Gaussian assumption.”
• Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients (2015, unknown): “This task has been intensively studied since the 1990s, see in particular [14, 15, 20, 22] for general treatments.”
• Non-intrusive reduced order modeling of nonlinear problems using neural networks (2018, background): “A list of notable examples includes parameter estimation [6], topology optimization [5], optimal control [30] and uncertainty quantification [29].”
• 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].”
• Quantification of model uncertainty in RANS simulations: A review (2018, methodology): “, polynomial chaos expansion [60, 139], probabilis ic collocation method [140], or sparse grid method [141].”
• Least squares polynomial chaos expansion: A review of sampling strategies (2017, methodology): “Sampling-based techniques such as least squares approximation (LSA) [51, 44], pseudo-spectral collocation [72, 21], Monte Carlo sampling [72], and compressive sampling [27, 46] have been employed in the literature to identify the PC coefficients.”
• Bayesian inference with optimal maps (2011, methodology): “Higher moments can be evaluated using known formulas for the expectations of products of orthogonal polynomials [30, 52].”
• Stochastic Galerkin Methods for the Boltzmann-Poisson system (2019, unknown): “An overview of several UQ approaches for hyperbolic and kinetic equations in particular can be found in [6], [7], [8], [9], [10], [11].”
• Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis (2015, methodology): “Various uncertainty quantification techniques can be applied for this purpose [46].”
• Coherence motivated sampling and convergence analysis of least squares polynomial Chaos regression (2014, methodology): “Thermally Driven Cavity Flow Following [34, 2, 35, 36], we next consider a 2-D heat driven square cavity flow problem with uncertain wall temperature, as shown in Fig.”
• 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].”