Variational inference for nonlinear inverse problems via neural net kernels: comparison to Bayesian neural networks, application to topology optimization
type: Item
instance of: scholarly article
title: Variational inference for nonlinear inverse problems via neural net kernels: comparison to Bayesian neural networks, application to topology optimization
author: V. Keshavarzzadeh
author: Robert M. Kirby
author: Akil C. Narayan
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2022-10-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/2205.03681
Mathematics Subject Classification ID: 62F15
zbMATH DE Number: 7598909
zbMATH Keywords: Bayesian inference
zbMATH Keywords: variational inference
zbMATH Keywords: neural network-based kernels
zbMATH Keywords: Bayesian neural networks
Wikidata QID: Q114196704
describes a project that uses: DistMesh
describes a project that uses: BayesDA
MaRDI profile type: Publication
OpenAlex ID: W4280568114
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cites work: A Measure-Theoretic Computational Method for Inverse Sensitivity Problems I: Method and Analysis
cites work: A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion
cites work: Hessian-based adaptive sparse quadrature for infinite-dimensional Bayesian inverse problems
cites work: On the convergence of the Laplace approximation and noise-level-robustness of Laplace-based Monte Carlo methods for Bayesian inverse problems
cites work: Sparse, adaptive Smolyak quadratures for Bayesian inverse problems
cites work: Computational Higher Order Quasi-Monte Carlo Integration
cites work: Sparse-grid, reduced-basis Bayesian inversion: nonaffine-parametric nonlinear equations
cites work: Bayesian inference with optimal maps
cites work: Q4614105
cites work: Conditional path sampling of SDEs and the Langevin MCMC method
cites work: Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods
cites work: A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion
cites work: Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo
cites work: Emulation of higher-order tensors in manifold Monte Carlo methods for Bayesian inverse problems
cites work: Geometric MCMC for infinite-dimensional inverse problems
cites work: Data-driven model reduction for the Bayesian solution of inverse problems
cites work: Accelerating Markov chain Monte Carlo with active subspaces
cites work: Metropolized Randomized Maximum Likelihood for Improved Sampling from Multimodal Distributions
cites work: A Randomized Maximum A Posteriori Method for Posterior Sampling of High Dimensional Nonlinear Bayesian Inverse Problems
cites work: Scalable Optimization-Based Sampling on Function Space
cites work: Stochastic spectral methods for efficient Bayesian solution of inverse problems
cites work: Q5268658
cites work: Sparse deterministic approximation of Bayesian inverse problems
cites work: Multilevel Adaptive Sparse Leja Approximations for Bayesian Inverse Problems
cites work: Using Bayesian statistics in the estimation of heat source in radiation
cites work: Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems
cites work: A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data
cites work: Quasi-Monte Carlo and Multilevel Monte Carlo Methods for Computing Posterior Expectations in Elliptic Inverse Problems
cites work: Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization
cites work: A stochastic collocation algorithm with multifidelity models
cites work: Stress-based topology optimization under uncertainty via simulation-based Gaussian process
cites work: Robust topology optimization with low rank approximation using artificial neural networks
cites work: Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian processes
cites work: Bayesian neural networks for uncertainty quantification in data-driven materials modeling
cites work: Inverse problems: a Bayesian perspective
cites work: Q4226179
cites work: Neural-net-induced Gaussian process regression for function approximation and PDE solution
cites work: Kernel flows: from learning kernels from data into the abyss
cites work: The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions
cites work: Gradient based design optimization under uncertainty via stochastic expansion methods
cites work: Numerical Integration in Multiple Dimensions with Designed Quadrature
cites work: A Simple Mesh Generator in MATLAB
cites work: Solution of the nonlinear elasticity imaging inverse problem: the incompressible case
cites work: Sparse variational Bayesian approximations for nonlinear inverse problems: applications in nonlinear elastography
cites work: Solution of the nonlinear elasticity imaging inverse problem: the compressible case
DOI: 10.1016/J.CMA.2022.115495
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description: scientific article; zbMATH DE number 7598909