Data-driven model reduction for the Bayesian solution of inverse problems

DOI10.1002/nme.4748zbMath1352.65445arXiv1403.4290OpenAlexW3121471846MaRDI QIDQ2952708

Karen Willcox, Youssef M. Marzouk, Tiangang Cui

Publication date: 30 December 2016

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.4290

zbMATH Keywords

inverse problem model reduction adaptive Markov chain Monte Carlo approximate Bayesian inference

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Related Items

Nonlinear sparse Bayesian learning for physics-based models, Learning physics-based models from data: perspectives from inverse problems and model reduction, Randomized approaches to accelerate MCMC algorithms for Bayesian inverse problems, Bayesian model inversion using stochastic spectral embedding, Fast model updating coupling Bayesian inference and PGD model reduction, Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction, Sparse-grid, reduced-basis Bayesian inversion: nonaffine-parametric nonlinear equations, Sparse-grid, reduced-basis Bayesian inversion, Reduced modeling of unknown trajectories, Parameter estimation with model order reduction for elliptic differential equations, Unnamed Item, An Acceleration Strategy for Randomize-Then-Optimize Sampling Via Deep Neural Networks, Multilevel model reduction for uncertainty quantification in computational structural dynamics, Certified dimension reduction in nonlinear Bayesian inverse problems, An adaptive SVD-Krylov reduced order model for surrogate based structural shape optimization through isogeometric boundary element method, Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization, An iterative algorithm for POD basis adaptation in solving parametric convection-diffusion equations, Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression, VI-DGP: a variational inference method with deep generative prior for solving high-dimensional inverse problems, Numerical linear algebra in data assimilation, The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications, Geometric learning for computational mechanics. III: Physics-constrained response surface of geometrically nonlinear shells, Context-Aware Surrogate Modeling for Balancing Approximation and Sampling Costs in Multifidelity Importance Sampling and Bayesian Inverse Problems, Reduced-order model-based variational inference with normalizing flows for Bayesian elliptic inverse problems, A greedy sensor selection algorithm for hyperparameterized linear Bayesian inverse problems with correlated noise models, Residual-based error correction for neural operator accelerated Infinite-dimensional Bayesian inverse problems, Scalable conditional deep inverse Rosenblatt transports using tensor trains and gradient-based dimension reduction, Deep Importance Sampling Using Tensor Trains with Application to a Priori and a Posteriori Rare Events, A low-rank solver for parameter estimation and uncertainty quantification in time-dependent systems of partial differential equations, Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems, Structured Bayesian Gaussian process latent variable model: applications to data-driven dimensionality reduction and high-dimensional inversion, Bayesian inversion for steady flow in fractured porous media with contact on fractures and hydro-mechanical coupling, An adaptive reduced basis ANOVA method for high-dimensional Bayesian inverse problems, A physics-aware, probabilistic machine learning framework for coarse-graining high-dimensional systems in the small data regime, A Hybrid Adaptive MCMC Algorithm in Function Spaces, Reduced Basis Methods for Uncertainty Quantification, Efficient State/Parameter Estimation in Nonlinear Unsteady PDEs by a Reduced Basis Ensemble Kalman Filter, Bayesian Mesh Adaptation for Estimating Distributed Parameters, An adaptive local reduced basis method for solving PDEs with uncertain inputs and evaluating risk, Accelerating MCMC via Kriging-based adaptive independent proposals and delayed rejection, Bayesian approach to inverse time-harmonic acoustic obstacle scattering with phaseless data generated by point source waves, Randomized reduced forward models for efficient Metropolis-Hastings MCMC, with application to subsurface fluid flow and capacitance tomography, Magnetic Resonance Electrical Impedance Tomography (MREIT): Convergence and Reduced Basis Approach, Local search methods for the solution of implicit inverse problems, Multifidelity Approximate Bayesian Computation, Adaptive Sparse Grid Model Order Reduction for Fast Bayesian Estimation and Inversion, A non-intrusive reduced basis EKI for time fractional diffusion inverse problems, Data-driven forward discretizations for Bayesian inversion, A transport-based multifidelity preconditioner for Markov chain Monte Carlo, Polynomial surrogates for Bayesian traveltime tomography, Low-rank dynamic mode decomposition: an exact and tractable solution, Optimal Model Management for Multifidelity Monte Carlo Estimation, Bayesian Model and Dimension Reduction for Uncertainty Propagation: Applications in Random Media, A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates, Stein Variational Reduced Basis Bayesian Inversion, Gaussian process regression and conditional polynomial chaos for parameter estimation, Variational inference for nonlinear inverse problems via neural net kernels: comparison to Bayesian neural networks, application to topology optimization, A generalized probabilistic learning approach for multi-fidelity uncertainty quantification in complex physical simulations, Stochastic Collocation Algorithms Using $l_1$-Minimization for Bayesian Solution of Inverse Problems, Deep composition of tensor-trains using squared inverse Rosenblatt transports, Convergence of spectral likelihood approximation based on q-Hermite polynomials for Bayesian inverse problems, Multi-frequency model reduction for uncertainty quantification in computational vibroacoutics

Cites Work