Multifidelity approaches for uncertainty quantification

[1]  Lambros S. Katafygiotis,et al.  Geometric insight into the challenges of solving high-dimensional reliability problems , 2008 .

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

[3]  Klaus Ritter,et al.  Multilevel Monte Carlo Approximation of Distribution Functions and Densities , 2015, SIAM/ASA J. Uncertain. Quantification.

[4]  Benjamin Peherstorfer,et al.  Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices , 2018, SIAM/ASA J. Uncertain. Quantification.

[5]  Fabio Nobile,et al.  Multi-index Monte Carlo: when sparsity meets sampling , 2014, Numerische Mathematik.

[6]  Christian Reeps,et al.  Correlation of biomechanics to tissue reaction in aortic aneurysms assessed by finite elements and [18F]–fluorodeoxyglucose–PET/CT , 2012, International journal for numerical methods in biomedical engineering.

[7]  Loic Le Gratiet,et al.  RECURSIVE CO-KRIGING MODEL FOR DESIGN OF COMPUTER EXPERIMENTS WITH MULTIPLE LEVELS OF FIDELITY , 2012, 1210.0686.

[8]  Wilson H. Tang,et al.  Optimal Importance‐Sampling Density Estimator , 1992 .

[9]  Benjamin Peherstorfer,et al.  Combining multiple surrogate models to accelerate failure probability estimation with expensive high-fidelity models , 2017, J. Comput. Phys..

[10]  Loic Le Gratiet,et al.  Bayesian Analysis of Hierarchical Multifidelity Codes , 2011, SIAM/ASA J. Uncertain. Quantification.

[11]  Nicholas Zabaras,et al.  Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification , 2018, J. Comput. Phys..

[12]  E. Hisdal.  Conditional possibilities independence and noninteraction , 1978 .

[13]  Ilias Bilionis,et al.  Multi-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification , 2013, J. Comput. Phys..

[14]  Jan S. Hesthaven,et al.  Reduced order modeling for nonlinear structural analysis using Gaussian process regression , 2018, Computer Methods in Applied Mechanics and Engineering.

[15]  F. Chinesta,et al.  A Short Review in Model Order Reduction Based on Proper Generalized Decomposition , 2018 .

[16]  J. Beck,et al.  Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation , 2001 .

[17]  Phaedon-Stelios Koutsourelakis,et al.  A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters , 2008, J. Comput. Phys..

[18]  Tiangang Cui,et al.  Multifidelity importance sampling , 2016 .

[19]  Xiang Ma,et al.  An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations , 2009, J. Comput. Phys..

[20]  Ahmed K. Noor,et al.  Reduced Basis Technique for Nonlinear Analysis of Structures , 1980 .

[21]  N. Wiener.  The Homogeneous Chaos , 1938 .

[22]  Robert Scheichl,et al.  Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and Its Application to Multilevel Monte Carlo Methods , 2013, SIAM J. Numer. Anal..

[23]  Alexey Chernov,et al.  Approximation of probability density functions by the Multilevel Monte Carlo Maximum Entropy method , 2016, J. Comput. Phys..

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

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

[26]  A. Patera,et al.  Certified real‐time solution of the parametrized steady incompressible Navier–Stokes equations: rigorous reduced‐basis a posteriori error bounds , 2005 .

[27]  George E. Karniadakis,et al.  Hidden physics models: Machine learning of nonlinear partial differential equations , 2017, J. Comput. Phys..

[28]  S. Brunton,et al.  Discovering governing equations from data by sparse identification of nonlinear dynamical systems , 2015, Proceedings of the National Academy of Sciences.

[29]  J. Beck,et al.  Important sampling in high dimensions , 2003 .

[30]  Tamara G. Kolda,et al.  An overview of the Trilinos project , 2005, TOMS.

[31]  Siddhartha Mishra,et al.  Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data , 2012, Math. Comput..

[32]  Jonas Sukys,et al.  Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions , 2012, J. Comput. Phys..

[33]  Ilias Bilionis,et al.  Multi-output local Gaussian process regression: Applications to uncertainty quantification , 2012, J. Comput. Phys..

[34]  Christian Reeps,et al.  The impact of model assumptions on results of computational mechanics in abdominal aortic aneurysm. , 2010, Journal of vascular surgery.

[35]  Phaedon-Stelios Koutsourelakis,et al.  Bayesian Model and Dimension Reduction for Uncertainty Propagation: Applications in Random Media , 2017, SIAM/ASA J. Uncertain. Quantification.

[36]  P. Eberhard,et al.  Using augmented Lagrangian particle swarm optimization for constrained problems in engineering">Using augmented Lagrangian particle swarm optimization for constrained problems in engineering , 2006 .

[37]  J. Beck,et al.  A new adaptive importance sampling scheme for reliability calculations , 1999 .

[38]  A. Chatterjee.  An introduction to the proper orthogonal decomposition , 2000 .

[39]  Andreas C. Damianou,et al.  Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling , 2017, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[40]  Ilias Bilionis,et al.  Multidimensional Adaptive Relevance Vector Machines for Uncertainty Quantification , 2012, SIAM J. Sci. Comput..

[41]  Florian Müller,et al.  Multilevel Monte Carlo for two phase flow and transport in random heterogeneous porous media , 2012 .

[42]  Didier Dubois,et al.  Random sets and fuzzy interval analysis , 1991 .

[43]  Christian Reeps,et al.  Probabilistic noninvasive prediction of wall properties of abdominal aortic aneurysms using Bayesian regression , 2017, Biomechanics and modeling in mechanobiology.

[44]  W. Wall,et al.  Towards efficient uncertainty quantification in complex and large-scale biomechanical problems based on a Bayesian multi-fidelity scheme , 2014, Biomechanics and Modeling in Mechanobiology.

[45]  Phaedon-Stelios Koutsourelakis,et al.  Accurate Uncertainty Quantification Using Inaccurate Computational Models , 2009, SIAM J. Sci. Comput..

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

[47]  J. Peraire,et al.  Balanced Model Reduction via the Proper Orthogonal Decomposition , 2002 .

[48]  Shawn E. Gano,et al.  Hybrid Variable Fidelity Optimization by Using a Kriging-Based Scaling Function , 2005 .

[49]  Iason Papaioannou,et al.  Multilevel Estimation of Rare Events , 2015, SIAM/ASA J. Uncertain. Quantification.

[50]  C. Bucher.  Adaptive sampling — an iterative fast Monte Carlo procedure , 1988 .