Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Stochastic partial differential equations: a modeling, white noise functional approach
Stochastic partial differential equations: a modeling, white noise functional approach
Stochastic analysis
Optimization by Vector Space Methods
Optimization by Vector Space Methods
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
SIAM Journal on Matrix Analysis and Applications
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
Algorithm 862: MATLAB tensor classes for fast algorithm prototyping
ACM Transactions on Mathematical Software (TOMS)
Stochastic spectral methods for efficient Bayesian solution of inverse problems
Journal of Computational Physics
Generalized spectral decomposition for stochastic nonlinear problems
Journal of Computational Physics
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
Journal of Computational Physics
A generalized polynomial chaos based ensemble Kalman filter with high accuracy
Journal of Computational Physics
Identification of Bayesian posteriors for coefficients of chaos expansions
Journal of Computational Physics
Bayesian inference with optimal maps
Journal of Computational Physics
| Hi-index | 31.45 |
We present a fully deterministic approach to a probabilistic interpretation of inverse problems in which unknown quantities are represented by random fields or processes, described by possibly non-Gaussian distributions. The description of the introduced random fields is given in a ''white noise'' framework, which enables us to solve the stochastic forward problem through Galerkin projection onto polynomial chaos. With the help of such a representation the probabilistic identification problem is cast in a polynomial chaos expansion setting and the Baye's linear form of updating. By introducing the Hermite algebra this becomes a direct, purely algebraic way of computing the posterior, which is comparatively inexpensive to evaluate. In addition, we show that the well-known Kalman filter is the low order part of this update. The proposed method is here tested on a stationary diffusion equation with prescribed source terms, characterised by an uncertain conductivity parameter which is then identified from limited and noisy data obtained by a measurement of the diffusing quantity.