Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Graphical models for machine learning and digital communication
Graphical models for machine learning and digital communication
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: modeling, learning, sampling and computing, Part I
Stereo Matching Using Belief Propagation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Gaussian Markov Random Fields: Theory And Applications (Monographs on Statistics and Applied Probability)
Mixed Discontinuous Galerkin Methods for Darcy Flow
Journal of Scientific Computing
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Journal of Computational Physics
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning
Nonparametric belief propagation
Communications of the ACM
The Probabilistic Program Dependence Graph and Its Application to Fault Diagnosis
IEEE Transactions on Software Engineering
PAMPAS: real-valued graphical models for computer vision
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Tree-based reparameterization framework for analysis of sum-product and related algorithms
IEEE Transactions on Information Theory
Multi-output local Gaussian process regression: Applications to uncertainty quantification
Journal of Computational Physics
A probabilistic graphical model approach to stochastic multiscale partial differential equations
Journal of Computational Physics
| Hi-index | 31.45 |
A probabilistic graphical model approach to uncertainty quantification for flows in random porous media is introduced. Model reduction techniques are used locally in the graph to represent the random permeability. Then the conditional distribution of the multi-output responses on the low dimensional representation of the permeability field is factorized into a product of local potential functions. An expectation-maximization algorithm is used to learn the nonparametric representation of these potentials using the given input/output data. We develop a nonparametric belief propagation method for uncertainty quantification by employing the loopy belief propagation algorithm. The nonparametric nature of our model is able to capture non-Gaussian features of the response. The proposed framework can be used as a surrogate model to predict the responses for new input realizations as well as our confidence on these predictions. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed framework for solving uncertainty quantification problems in flows through porous media using stationary and non-stationary permeability fields.