A robust and efficient stepwise regression method for building sparse polynomial chaos expansions, Journal of Computational Physics, vol.332, pp.461-474, 2017. ,
Identification of bayesian posteriors for coefficients of chaos expansions, Journal of Computational Physics, pp.3134-3154, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00684317
Stochastic finite element: a non intrusive approach by regression, European Journal of Computational Mechanics/Revue Européenne de Mécanique Numérique, vol.15, pp.81-92, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-01665506
Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach, Comptes Rendus Mécanique, vol.336, pp.518-523, 2008. ,
Adaptive sparse polynomial chaos expansion based on least angle regression, Journal of Computational Physics, vol.230, pp.2345-2367, 2011. ,
Applied Smoothing Techniques for Data Analysis, 1997. ,
Bayesian Methods for Data Analysis, 2008. ,
Parameter estimation using polynomial chaos and maximum likelihood, International Journal of Computer Mathematics, vol.91, pp.336-346, 2014. ,
, Bayesian Statistical Modelling, vol.704, 2007.
Polynomial chaos representation of spatio-temporal random fields from experimental measurements, Journal of Computational Physics, vol.228, pp.8726-8751, 2009. ,
Asymptotic sampling distribution for polynomial chaos representation from data: a maximum entropy and fisher information approach, SIAM Journal on Scientific Computing, vol.30, pp.2207-2234, 2008. ,
Numerical challenges in the use of polynomial chaos representations for stochastic processes, SIAM journal on scientific computing, vol.26, pp.698-719, 2004. ,
Maximum likelihood estimation of stochastic chaos representations from experimental data, International Journal for Numerical Methods in Engineering, vol.66, pp.978-1001, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00686154
Identification of chaos representations of elastic properties of random media using experimental vibration tests, Computational mechanics, vol.39, pp.831-838, 2007. ,
Stochastic model reduction for chaos representations, Computer Methods in Applied Mechanics and Engineering, vol.196, pp.3951-3966, 2007. ,
On the convergence of generalized polynomial chaos expansions, ESAIM: Mathematical Modelling and Numerical Analysis, vol.46, pp.317-339, 2012. ,
, Handbook of Uncertainty Quantification, vol.1, 2017.
On the construction and analysis of stochastic models: characterization and propagation of the errors associated with limited data, Journal of Computational Physics, vol.217, pp.63-81, 2006. ,
Red-Horse, A probabilistic construction of model validation, Computer Methods in Applied Mechanics and Engineering, vol.197, pp.2585-2595, 2008. ,
, Stochastic Finite Elements: a Spectral Approach, 1991.
Stochastic convergence acceleration through basis enrichment of polynomial chaos expansions, International journal for numerical methods in engineering, vol.73, pp.162-184, 2008. ,
, Computational Statistics, 2013.
Theoretical framework and experimental procedure for modelling mesoscopic volume fraction stochastic fluctuations in fiber reinforced composites, International Journal of Solids and Structures, vol.45, pp.5567-5583, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00684818
, Statistical and Computational Inverse Problems, vol.160, 2005.
, Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics, 2010.
Uncertainty propagation using wiener-haar expansions, Journal of computational Physics, vol.197, pp.28-57, 2004. ,
Generalized polynomial chaos and random oscillators, International Journal for Numerical Methods in Engineering, vol.60, pp.571-596, 2004. ,
Symmetric functions and Hall polynomials 2nd Ed, 2015. ,
Polynomial-chaos-based bayesian approach for state and parameter estimations, Journal of Guidance, Control, and Dynamics, vol.36, pp.1058-1074, 2013. ,
Surrogate models for oscillatory systems using sparse polynomial chaos expansions and stochastic time warping, SIAM/ASA Journal on Uncertainty Quantification, vol.5, pp.540-571, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01421106
Dimensionality reduction and polynomial chaos acceleration of bayesian inference in inverse problems, Journal of Computational Physics, vol.228, pp.1862-1902, 2009. ,
Stochastic spectral methods for efficient bayesian solution of inverse problems, Journal of Computational Physics, vol.224, pp.560-586, 2007. ,
Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics, Annual review of fluid mechanics, vol.41, pp.35-52, 2009. ,
Random field representations for stochastic elliptic boundary value problems and statistical inverse problems, European Journal of Applied Mathematics, vol.25, pp.339-373, 2014. ,
Identification of polynomial chaos representations in high dimension from a set of realizations, SIAM Journal on Scientific Computing, vol.34, pp.2917-2945, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00770006
Karhunen-loève expansion revisited for vector-valued random fields: Scaling, errors and optimal basis, Journal of Computational Physics, pp.607-622, 2013. ,
Non-gaussian simulation using hermite polynomial expansion: convergences and algorithms, Probabilistic Engineering Mechanics, vol.17, pp.10-13, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-00686282
Sampling-free linear bayesian update of polynomial chaos representations, Journal of Computational Physics, pp.5761-5787, 2012. ,
Simulation and the Monte Carlo Method, 2008. ,
Approximation theorems of mathematical statistics, vol.162, 1980. ,
Bayesian sparse polynomial chaos expansion for global sensitivity analysis, Computer Methods in Applied Mechanics and Engineering, vol.318, pp.474-496, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01476649
Identification of high-dimension polynomial chaos expansions with random coefficients for non-gaussian tensor-valued random fields using partial and limited experimental data, Computer methods in applied mechanics and engineering, vol.199, pp.2150-2164, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00684324
A computational inverse method for identification of non-gaussian random fields using the bayesian approach in very high dimension, Computer Methods in Applied Mechanics and Engineering, vol.200, pp.3083-3099, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00684294
Polynomial chaos expansion of a multimodal random vector, SIAM/ASA Journal on Uncertainty Quantification, vol.3, pp.34-60, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01105959
Uncertainty Quantification. An Accelerated Course with Advanced Applications in Computational Engineering, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-00826082
Computational aspects for constructing realizations of polynomial chaos in high dimension, SIAM Journal on Scientific Computing, vol.32, pp.2820-2831, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00684323
Physical systems with random uncertainties: chaos representations with arbitrary probability measure, SIAM Journal on Scientific Computing, vol.26, pp.395-410, 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-00686211
Reduced chaos decomposition with random coefficients of vectorvalued random variables and random fields, Computer Methods in Applied Mechanics and Engineering, vol.198, pp.1926-1934, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00684487
Introduction to Stochastic Searh and Optimization ,
Coordinate transformation and polynomial chaos for the bayesian inference of a gaussian process with parametrized prior covariance function, Computer Methods in Applied Mechanics and Engineering, vol.298, pp.205-228, 2016. ,
Inverse problems: a bayesian perspective, Acta numerica, vol.19, pp.451-559, 2010. ,
Inverse Problem Theory And Methods For Model Parameter Estimation, vol.89, 2005. ,
Variable kernel density estimation, The Annals of Statistics, vol.20, pp.1236-1265, 1992. ,
Homogeneous chaos basis adaptation for design optimization under uncertainty: Application to the oil well placement problem, Artificial Intelligence for Engineering Design, pp.265-276, 2017. ,
Basis adaptation in homogeneous chaos spaces, Journal of Computational Physics, vol.259, pp.304-317, 2014. ,
Bayesian adaptation of chaos representations using variational inference and sampling on geodesics, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.474, p.20180285, 2018. ,
Reduced wiener chaos representation of random fields via basis adaptation and projection, Journal of Computational Physics, pp.102-120, 2017. ,
Multi-element generalized polynomial chaos for arbitrary probability measures, SIAM Journal on Scientific Computing, vol.28, pp.901-928, 2006. ,
The wiener-askey polynomial chaos for stochastic differential equations, SIAM journal on scientific computing, vol.24, pp.619-644, 2002. ,