A probabilistic graphical model approach to stochastic multiscale partial differential equations

DOI10.1016/j.jcp.2013.05.016zbMath1349.65036OpenAlexW1964773554MaRDI QIDQ340925

Jiang Wan, Nicholas Zabaras

Publication date: 15 November 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2013.05.016

zbMATH Keywords

stochastic partial differential equationssequential Monte CarloBayesianprobabilistic graphical modelsuncertainty quantificationmultiscale modelingbelief propagation

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) PDEs with randomness, stochastic partial differential equations (35R60) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (13)

A nonparametric belief propagation method for uncertainty quantification with applications to flow in random porous media ⋮ A new network approach to Bayesian inference in partial differential equations ⋮ Cluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients ⋮ Reduced-order model-based variational inference with normalizing flows for Bayesian elliptic inverse problems ⋮ A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems ⋮ A Data-Driven Approach for Multiscale Elliptic PDEs with Random Coefficients Based on Intrinsic Dimension Reduction ⋮ Physics-Constrained, Data-Driven Discovery of Coarse-Grained Dynamics ⋮ A PCE-based multiscale framework for the characterization of uncertainties in complex systems ⋮ Parallel probabilistic graphical model approach for nonparametric Bayesian inference ⋮ A Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach ⋮ Uncertainty propagation using infinite mixture of gaussian processes and variational Bayesian inference ⋮ Digital-Image-Driven Stochastic Homogenization for Recycled Aggregate Concrete Based on Material Microstructure ⋮ A Bayesian multiscale deep learning framework for flows in random media

Uses Software

• GMRFLib
• PRMLT

Cites Work

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