Physics Information Aided Kriging using Stochastic Simulation Models

[1]  Xiu Yang,et al.  Reweighted ℓ1ℓ1 minimization method for stochastic elliptic differential equations , 2013, J. Comput. Phys..

[2]  Amine Bermak,et al.  Gaussian process for nonstationary time series prediction , 2004, Comput. Stat. Data Anal..

[3]  Xiu Yang,et al.  Adaptive ANOVA decomposition of stochastic incompressible and compressible flows , 2012, J. Comput. Phys..

[4]  Alexandre M. Tartakovsky,et al.  Immiscible front evolution in randomly heterogeneous porous media , 2003 .

[5]  M. Webb,et al.  Quantification of modelling uncertainties in a large ensemble of climate change simulations , 2004, Nature.

[6]  D. Ginsbourger,et al.  Additive Covariance Kernels for High-Dimensional Gaussian Process Modeling , 2011, 1111.6233.

[7]  Pierre Sagaut,et al.  A hybrid anchored-ANOVA - POD/Kriging method for uncertainty quantification in unsteady high-fidelity CFD simulations , 2016, J. Comput. Phys..

[8]  Michael B. Giles,et al.  Multilevel Monte Carlo Path Simulation , 2008, Oper. Res..

[9]  Ming Jian Zuo,et al.  A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis , 2018, Reliab. Eng. Syst. Saf..

[10]  Tag Gon Kim,et al.  Specification of multi-resolution modeling space for multi-resolution system simulation , 2013, Simul..

[11]  K. A. Cliffe,et al.  Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients , 2011, Comput. Vis. Sci..

[12]  Andrea Barth,et al.  Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients , 2011, Numerische Mathematik.

[13]  David A. Barajas-Solano,et al.  Physics-Informed CoKriging: A Gaussian-Process-Regression-Based Multifidelity Method for Data-Model Convergence , 2018, J. Comput. Phys..

[14]  David A. Cohn,et al.  Active Learning with Statistical Models , 1996, NIPS.

[15]  Guang Lin,et al.  An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media , 2009 .

[16]  Brian Berkowitz,et al.  Mixing-induced precipitation and porosity evolution in porous media , 2005 .

[17]  Dongbin Xiu,et al.  High-Order Collocation Methods for Differential Equations with Random Inputs , 2005, SIAM J. Sci. Comput..

[18]  A. O'Hagan,et al.  Predicting the output from a complex computer code when fast approximations are available , 2000 .

[19]  Daniele Venturi,et al.  Multi-fidelity Gaussian process regression for prediction of random fields , 2017, J. Comput. Phys..

[20]  Paris Perdikaris,et al.  Machine learning of linear differential equations using Gaussian processes , 2017, J. Comput. Phys..

[21]  Thomas J. Santner,et al.  Design and analysis of computer experiments , 1998 .

[22]  Alexey Chernov,et al.  Convergence analysis of multilevel Monte Carlo variance estimators and application for random obstacle problems , 2015, Numerische Mathematik.

[23]  Geir Evensen,et al.  The Ensemble Kalman Filter: theoretical formulation and practical implementation , 2003 .

[24]  Alexandre M. Tartakovsky,et al.  A Comparison of Closures for Stochastic Advection-Diffusion Equations , 2013, SIAM/ASA J. Uncertain. Quantification.

[25]  Houman Owhadi,et al.  Bayesian Numerical Homogenization , 2014, Multiscale Model. Simul..

[26]  Dongbin Xiu,et al.  Multi-fidelity stochastic collocation method for computation of statistical moments , 2017, J. Comput. Phys..