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A probabilistic graphical model approach to stochastic multiscale partial differential equations
15 references·1 citing·30 second hop
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References

  • 1974Spatial Interaction and the Statistical Analysis of Lattice Systems6,140 cited
  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data1,396 cited
  • 2005Gaussian Markov Random Fields: Theory and Applications1,219 cited
  • 2008A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data942 cited
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  • 2011Adaptive ANOVA decomposition of stochastic incompressible and compressible flows127 cited
  • 2006Bayesian-Optimal Design via Interacting Particle Systems

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101 cited
  • 2009A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters70 cited
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    • 2014Uncertainty quantification for multiscale disk forging of polycrystal materials using probabilistic graphical model techniques9 cited