Solution of physics-based Bayesian inverse problems with deep generative priors

DOI10.1016/j.cma.2022.115428OpenAlexW3182066884MaRDI QIDQ2083099

Assad A. Oberai, Dhruv Patel, Deep Ray

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/2107.02926

zbMATH Keywords

inverse problemsBayesian inferenceMarkov chain Monte Carlo (MCMC)elastographymodel order reductionuncertainty quantification (UQ)

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Bayesian inference (62F15)

Related Items

VI-DGP: a variational inference method with deep generative prior for solving high-dimensional inverse problems, Error estimates and physics informed augmentation of neural networks for thermally coupled incompressible Navier Stokes equations, Solution of physics-based inverse problems using conditional generative adversarial networks with full gradient penalty, A dimension-reduced variational approach for solving physics-based inverse problems using generative adversarial network priors and normalizing flows, Resolution-independent generative models based on operator learning for physics-constrained Bayesian inverse problems

Uses Software

• FEniCS
• MNIST
• TensorFlow
• NeuralUQ
• uq-vae
• NUTS
• Wasserstein GAN

Cites Work

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• The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo
• Constraint-aware neural networks for Riemann problems
• Source term identification for an axisymmetric inverse heat conduction problem
• Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
• Two-dimensional inverse heat conduction problem of source strength estimation in cylindrical rods
• Tikhonov regularization and the L-curve for large discrete ill-posed problems
• Evaluation of Gaussian approximations for data assimilation in reservoir models
• Adversarial uncertainty quantification in physics-informed neural networks
• The Mathematics of Computerized Tomography
• Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems
• An Introduction to the Mathematical Theory of Inverse Problems
• Handbook of Markov Chain Monte Carlo
• Structural identification of an unknown source term in a heat equation
• Resolution of seismic waveform inversion: Bayes versus Occam
• Electrical impedance tomography with basis constraints
• GAN-Based Priors for Quantifying Uncertainty in Supervised Learning
• Enforcing Imprecise Constraints on Generative Adversarial Networks for Emulating Physical Systems
• Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
• Priorconditioners for linear systems
• Inverse problems for partial differential equations
• An inverse problem for the heat equation