A generalized probabilistic learning approach for multi-fidelity uncertainty quantification in complex physical simulations

[1]  W. Hartt,et al.  Data-driven physics-informed constitutive metamodeling of complex fluids: A multifidelity neural network (MFNN) framework , 2021 .

[2]  George Em Karniadakis,et al.  Multi-fidelity Bayesian Neural Networks: Algorithms and Applications , 2020, J. Comput. Phys..

[3]  Liu Yang,et al.  B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data , 2020, J. Comput. Phys..

[4]  Katrin Ellermann,et al.  Bayesian Uncertainty Quantification with Multi-Fidelity Data and Gaussian Processes for Impedance Cardiography of Aortic Dissection , 2019, Entropy.

[5]  George Em Karniadakis,et al.  A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems , 2019, J. Comput. Phys..

[6]  Gianluca Geraci,et al.  A generalized approximate control variate framework for multifidelity uncertainty quantification , 2018, J. Comput. Phys..

[7]  Michael Hanss,et al.  Multifidelity approaches for uncertainty quantification , 2019, GAMM-Mitteilungen.

[8]  Seungjoon Lee,et al.  Linking Gaussian process regression with data-driven manifold embeddings for nonlinear data fusion , 2018, Interface Focus.

[9]  Paris Perdikaris,et al.  Adversarial Uncertainty Quantification in Physics-Informed Neural Networks , 2018, J. Comput. Phys..

[10]  Katharina Kormann,et al.  Fast Matrix-Free Evaluation of Discontinuous Galerkin Finite Element Operators , 2017, ACM Trans. Math. Softw..

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

[12]  David Wells,et al.  The deal.II library, Version 9.0 , 2018, J. Num. Math..

[13]  Benjamin Peherstorfer,et al.  Survey of multifidelity methods in uncertainty propagation, inference, and optimization , 2018, SIAM Rev..

[14]  A. Quaglino,et al.  Fast uncertainty quantification of activation sequences in patient‐specific cardiac electrophysiology meeting clinical time constraints , 2018, International journal for numerical methods in biomedical engineering.

[15]  Martin Kronbichler,et al.  Efficiency of high‐performance discontinuous Galerkin spectral element methods for under‐resolved turbulent incompressible flows , 2018, 1802.01439.

[16]  Martin Kronbichler,et al.  Robust and efficient discontinuous Galerkin methods for under-resolved turbulent incompressible flows , 2018, J. Comput. Phys..

[17]  Martin Kronbichler,et al.  On the stability of projection methods for the incompressible Navier-Stokes equations based on high-order discontinuous Galerkin discretizations , 2017, J. Comput. Phys..

[18]  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.

[19]  Paris Perdikaris,et al.  Inferring solutions of differential equations using noisy multi-fidelity data , 2016, J. Comput. Phys..

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

[21]  Wolfgang A. Wall,et al.  Unified computational framework for the efficient solution of n-field coupled problems with monolithic schemes , 2016, 1605.01522.

[22]  G. Karniadakis,et al.  Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond , 2016, Journal of The Royal Society Interface.

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

[24]  P Perdikaris,et al.  Multi-fidelity modelling via recursive co-kriging and Gaussian–Markov random fields , 2015, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[25]  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.

[26]  Michael B. Giles,et al.  Multilevel Monte Carlo methods , 2013, Acta Numerica.

[27]  Junjie Li,et al.  System probabilistic stability analysis of soil slopes using Gaussian process regression with Latin hypercube sampling , 2015 .

[28]  Jiming Liu,et al.  Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range , 2014, BMC Medical Research Methodology.

[29]  Tiangang Cui,et al.  Data‐driven model reduction for the Bayesian solution of inverse problems , 2014, 1403.4290.

[30]  Jinglai Li,et al.  Adaptive Construction of Surrogates for the Bayesian Solution of Inverse Problems , 2013, SIAM J. Sci. Comput..

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

[32]  N. Zabaras,et al.  Solution of inverse problems with limited forward solver evaluations: a Bayesian perspective , 2013 .

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

[34]  Oliver Schütze,et al.  PSA - A New Scalable Space Partition Based Selection Algorithm for MOEAs , 2012, EVOLVE.

[35]  Wolfgang A. Wall,et al.  Fluid–structure interaction for non-conforming interfaces based on a dual mortar formulation , 2011 .

[36]  Pritam Ranjan,et al.  A Computationally Stable Approach to Gaussian Process Interpolation of Deterministic Computer Simulation Data , 2010, Technometrics.

[37]  Wolfgang A. Wall,et al.  An embedded Dirichlet formulation for 3D continua , 2010 .

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

[39]  Rachel T. Johnson,et al.  Design and analysis for the Gaussian process model , 2009, Qual. Reliab. Eng. Int..

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

[41]  Geoff K. Nicholls,et al.  Sampling Conductivity Images via MCMC , 2007 .

[42]  C. Fox,et al.  Markov chain Monte Carlo Using an Approximation , 2005 .

[43]  Stefan Heinrich,et al.  Multilevel Monte Carlo Methods , 2001, LSSC.

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

[45]  L Tierney,et al.  Some adaptive monte carlo methods for Bayesian inference. , 1999, Statistics in medicine.

[46]  M. Veloso,et al.  Latent Variable Models , 2019, Statistical and Econometric Methods for Transportation Data Analysis.

[47]  R. Caflisch.  Monte Carlo and quasi-Monte Carlo methods , 1998, Acta Numerica.

[48]  D. Owen,et al.  Design of simple low order finite elements for large strain analysis of nearly incompressible solids , 1996 .

[49]  R. Rannacher,et al.  Benchmark Computations of Laminar Flow Around a Cylinder , 1996 .

[50]  I. M. Soboĺ.  Quasi-Monte Carlo methods , 1990 .