Variational inference for nonlinear inverse problems via neural net kernels: comparison to Bayesian neural networks, application to topology optimization

DOI10.1016/j.cma.2022.115495OpenAlexW4280568114WikidataQ114196704 ScholiaQ114196704MaRDI QIDQ2083125

Vahid Keshavarzzadeh, Akil C. Narayan, Robert M. Kirby

Publication date: 10 October 2022

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.03681

zbMATH Keywords

Bayesian inferencevariational inferenceBayesian neural networksneural network-based kernels

Mathematics Subject Classification ID

Bayesian inference (62F15)

Uses Software

• BayesDA
• DistMesh

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solution of the nonlinear elasticity imaging inverse problem: the incompressible case
• Bayesian inference with optimal maps
• Emulation of higher-order tensors in manifold Monte Carlo methods for Bayesian inverse problems
• Stochastic spectral methods for efficient Bayesian solution of inverse problems
• Geometric MCMC for infinite-dimensional inverse problems
• The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions
• Stress-based topology optimization under uncertainty via simulation-based Gaussian process
• On the convergence of the Laplace approximation and noise-level-robustness of Laplace-based Monte Carlo methods for Bayesian inverse problems
• Neural-net-induced Gaussian process regression for function approximation and PDE solution
• Kernel flows: from learning kernels from data into the abyss
• Bayesian neural networks for uncertainty quantification in data-driven materials modeling
• Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian processes
• Gradient based design optimization under uncertainty via stochastic expansion methods
• Hessian-based adaptive sparse quadrature for infinite-dimensional Bayesian inverse problems
• Sparse-grid, reduced-basis Bayesian inversion: nonaffine-parametric nonlinear equations
• Sparse variational Bayesian approximations for nonlinear inverse problems: applications in nonlinear elastography
• Using Bayesian statistics in the estimation of heat source in radiation
• Conditional path sampling of SDEs and the Langevin MCMC method
• Robust topology optimization with low rank approximation using artificial neural networks
• Accelerating Markov Chain Monte Carlo with Active Subspaces
• Sparse, adaptive Smolyak quadratures for Bayesian inverse problems
• A Stochastic Collocation Algorithm with Multifidelity Models
• Sparse deterministic approximation of Bayesian inverse problems
• Inverse problems: A Bayesian perspective
• A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion
• Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo
• Data-driven model reduction for the Bayesian solution of inverse problems
• Computational Higher Order Quasi-Monte Carlo Integration
• Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems
• A Measure-Theoretic Computational Method for Inverse Sensitivity Problems I: Method and Analysis
• A Randomized Maximum A Posteriori Method for Posterior Sampling of High Dimensional Nonlinear Bayesian Inverse Problems
• Numerical Integration in Multiple Dimensions with Designed Quadrature
• A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• Solution of the nonlinear elasticity imaging inverse problem: the compressible case
• Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization
• Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods
• A Simple Mesh Generator in MATLAB
• Scalable Optimization-Based Sampling on Function Space
• Multilevel Adaptive Sparse Leja Approximations for Bayesian Inverse Problems
• Metropolized Randomized Maximum Likelihood for Improved Sampling from Multimodal Distributions
• Quasi-Monte Carlo and Multilevel Monte Carlo Methods for Computing Posterior Expectations in Elliptic Inverse Problems
• A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion

This page was built for publication: Variational inference for nonlinear inverse problems via neural net kernels: comparison to Bayesian neural networks, application to topology optimization