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Bayesian Adaptive Polynomial Chaos Expansions
Polynomial chaos expansions (PCE) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully Bayesian formulations remain rare, especially with implementations in R.
Rumsey, Kellin N. +4 more
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Uncertainty quantification (UQ) [PDF]
, 2011 This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece.
3rd Micro and Nano Flows Conference (MNF2011) +1 more
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Polynomial Chaos Expansion of a Multimodal Random Vector [PDF]
SIAM/ASA Journal on Uncertainty Quantification, 2015 A methodology and algorithms are proposed for constructing the polynomial chaos expansion (PCE) of multimodal random vectors. An algorithm is developed for generating independent realizations of any multimodal multivariate probability measure that is constructed from a set of independent realizations using the Gaussian kernel-density estimation method.
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Meta-models for structural reliability and uncertainty quantification [PDF]
, 2011 A meta-model (or a surrogate model) is the modern name for what was traditionally called a response surface. It is intended to mimic the behaviour of a computational model M (e.g.
Sudret, Bruno
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, 2017 In this paper, we develop a numerical approach based on Chaos expansions to analyze the sensitivity and the propagation of epistemic uncertainty through a queueing systems with breakdowns.
Abbas, Karim +3 more
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Parameter Estimation for Mechanical Systems Using an Extended Kalman Filter [PDF]
, 2008 This paper proposes a new computational approach based on the Extended Kalman Filter (EKF) in order to apply the polynomial chaos theory to the problem of parameter estimation, using direct stochastic collocation.
Blanchard, Emmanuel +2 more
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Sensors, 2017 A microstructure beam is one of the fundamental elements in MEMS devices like cantilever sensors, RF/optical switches, varactors, resonators, etc.
Lili Gao, Zai-Fa Zhou, Qing-An Huang
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Simulation of Stochastic Quantum Systems Using Polynomial Chaos Expansions
Physical Review Letters, 2013 We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertainty quantification. The polynomial chaos expansion represents the system density matrix as a series of orthogonal polynomials in the principle components of ...
Young, Kevin C., Grace, Matthew D.
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Polynomial Chaos Expansion for Operator Learning
Operator learning (OL) has emerged as a powerful tool in scientific machine learning (SciML) for approximating mappings between infinite-dimensional functional spaces. One of its main applications is learning the solution operator of partial differential equations (PDEs).
Sharma, Himanshu +2 more
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A polynomial chaos expansion in dependent random variables
Journal of Mathematical Analysis and Applications, 2018 26 pages, three figures, four tables; accepted by Journal of Mathematical Analysis and Applications.
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