Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes

By Bert J. Debusschere, Habib N. Najm, Philippe P. Pébay, Omar M. Knio, Roger G. Ghanem, O. L. Le Maître. SIAM Journal on Scientific Computing, 2005

478 citations recorded by the source corpus.

Subfields: Environmental Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/571cff12cdc81fc27cbdc80485fe1e73cbf0bdef

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Citations in the corpus

Asynchronous Time Integration for Polynomial Chaos Expansion of Uncertain Periodic Dynamics (2010, methodology): “These projections are performed by means of pseudo-spectral techniques (see [5]).”
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].”
Chaospy: An open source tool for designing methods of uncertainty quantification (2015, background): “As far as the authors know, there are only a few viable options for the latter class of methods: The Dakota Project (referred to as Dakota) [3], the Opus Open Turns library (referred to as Turns) [4], Uncertenty Quantification Toolkit [5], and MIT Uncertenty Quantification Library [6].”
Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009, background): “These evaluations may be easy for certain types of nonlinearities (simple form of the nonlinear operator) [34, 71, 72].”
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems (2008, background): “These operations are incorporated into a library for “stochastic arithmetic,” detailed in [11].”
Uncertainty quantification in chemical systems (2009, methodology): “where the right-hand side can be evaluated using spectral or pseudo-spectral constructions [59].”
Stochastic Analysis of Multiconductor Cables and Interconnects (2011, background): “It is based on the so-called polynomial chaos (PC) technique that assumes a series of orthogonal polynomials of random variables for the description of the solution of a stochastic problem [2]–[4].”
Optimizing User Satisfaction of Mobile Workloads Subject to Various Sources of Uncertainties (2019, background): “The generalized polynomial chaos expansion (gPCE) [25], [26], [27] represents yðtÞ as a multivariate polynomial P cifiðXðtÞÞ in which ci are the unknown coefficients that must be estimated from sample data, and fiðXðtÞÞ are orthogonal basis functions that are determined by the distributions of the r”
Dynamically orthogonal field equations for continuous stochastic dynamical systems (2009, background): “[46,47,63,48,64]) are usually derived by substituting a representation as (7) but with the stochastic coefficients given by (23) to the SPDE (8) and then projecting it to the stochastic orthogonal basis functionsΦj(ζ(ω)) using the inner product.”