VI-DGP: a variational inference method with deep generative prior for solving high-dimensional inverse problems

DOI10.1007/s10915-023-02328-warXiv2302.11173OpenAlexW4386526483MaRDI QIDQ6053024

Yingzhi Xia, Jinglai Li, Qifeng Liao

Publication date: 25 September 2023

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2302.11173

zbMATH Keywords

inverse problemsgradient approximationvariational inferencedeep generative modelphysics-constrained surrogate

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Bayesian inference (62F15) Numerical solution to inverse problems in abstract spaces (65J22)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multi-output separable Gaussian process: towards an efficient, fully Bayesian paradigm for uncertainty quantification
• Spectral gaps for a Metropolis-Hastings algorithm in infinite dimensions
• Stochastic spectral methods for efficient Bayesian solution of inverse problems
• Bayesian and variational Bayesian approaches for flows in heterogeneous random media
• Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification
• Statistical and computational inverse problems.
• Stochastic reduced order models for inverse problems under uncertainty
• Modeling uncertainty in flow simulations via generalized polynomial chaos.
• Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification
• Deep generative modeling for mechanistic-based learning and design of metamaterial systems
• Iterative surrogate model optimization (ISMO): an active learning algorithm for PDE constrained optimization with deep neural networks
• Solution of physics-based Bayesian inverse problems with deep generative priors
• A deep domain decomposition method based on Fourier features
• Solving inverse problems using conditional invertible neural networks
• Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems
• Solving inverse wave scattering with deep learning
• Variational Bayesian approximation of inverse problems using sparse precision matrices
• Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data
• Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
• Approximate Bayesian model inversion for PDEs with heterogeneous and state-dependent coefficients
• An adaptive reduced basis ANOVA method for high-dimensional Bayesian inverse problems
• Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks
• Stein variational gradient descent with local approximations
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• A variational Bayesian approach for inverse problems with skew-\(t\) error distributions
• 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
• A Bayesian approach to multiscale inverse problems using the sequential Monte Carlo method
• A Randomized Maximum A Posteriori Method for Posterior Sampling of High Dimensional Nonlinear Bayesian Inverse Problems
• Inverse Problem Theory and Methods for Model Parameter Estimation
• Stein Variational Reduced Basis Bayesian Inversion
• Equation of State Calculations by Fast Computing Machines
• SwitchNet: A Neural Network Model for Forward and Inverse Scattering Problems
• Variational Bayes' Method for Functions with Applications to Some Inverse Problems
• MCMC methods for functions: modifying old algorithms to make them faster

This page was built for publication: VI-DGP: a variational inference method with deep generative prior for solving high-dimensional inverse problems