Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
RKC: an explicit solver for parabolic PDEs
Journal of Computational and Applied Mathematics
Comparison of approximate methods for handling hyperparameters
Neural Computation
A stochastic projection method for fluid flow. I: basic formulation
Journal of Computational Physics
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
A stochastic projection method for fluid flow II.: random process
Journal of Computational Physics
A variational finite element method for source inversion for convective-diffusive transport
Finite Elements in Analysis and Design - Special issue: 14th Robert J. Melosh competition
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
SIAM Journal on Scientific Computing
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Hermite expansions in Monte-Carlo computation
Journal of Computational Physics
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
Journal of Computational Physics
Identification of Bayesian posteriors for coefficients of chaos expansions
Journal of Computational Physics
Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems
SIAM Journal on Scientific Computing
Automatica (Journal of IFAC)
A variational Bayesian method to inverse problems with impulsive noise
Journal of Computational Physics
A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Expansions
SIAM Journal on Scientific Computing
Sampling-free linear Bayesian update of polynomial chaos representations
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A Posteriori Error Analysis of Parameterized Linear Systems Using Spectral Methods
SIAM Journal on Matrix Analysis and Applications
Bayesian inference with optimal maps
Journal of Computational Physics
Simulation-based optimal Bayesian experimental design for nonlinear systems
Journal of Computational Physics
Multiparameter Spectral Representation of Noise-Induced Competence in Bacillus Subtilis
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Ensemble level multiscale finite element and preconditioner for channelized systems and applications
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Hi-index | 31.48 |
We present a reformulation of the Bayesian approach to inverse problems, that seeks to accelerate Bayesian inference by using polynomial chaos (PC) expansions to represent random variables. Evaluation of integrals over the unknown parameter space is recast, more efficiently, as Monte Carlo sampling of the random variables underlying the PC expansion. We evaluate the utility of this technique on a transient diffusion problem arising in contaminant source inversion. The accuracy of posterior estimates is examined with respect to the order of the PC representation, the choice of PC basis, and the decomposition of the support of the prior. The computational cost of the new scheme shows significant gains over direct sampling.