Data-driven forward discretizations for Bayesian inversion

DOI10.1088/1361-6420/abb2fazbMath1450.62136arXiv2003.07991OpenAlexW3080853598MaRDI QIDQ4970560

Daniele Bigoni, Yuming Chen, Daniel Sanz-Alonso, Youssef M. Marzouk, Nicolás García Trillos

Publication date: 7 October 2020

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.07991

zbMATH Keywords

Bayesian inverse problemshierarchical learningdata-driven discretizations

Mathematics Subject Classification ID

Computational methods for problems pertaining to statistics (62-08) Bayesian inference (62F15) Learning and adaptive systems in artificial intelligence (68T05) Applications of statistics to physics (62P35)

Related Items (4)

Analysis of a Computational Framework for Bayesian Inverse Problems: Ensemble Kalman Updates and MAP Estimators under Mesh Refinement ⋮ The Random Feature Model for Input-Output Maps between Banach Spaces ⋮ The SPDE approach to Matérn fields: graph representations ⋮ Graph-based prior and forward models for inverse problems on manifolds with boundaries

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
• Stochastic spectral methods for efficient Bayesian solution of inverse problems
• Design and analysis of computer experiments. With comments and a rejoinder by the authors
• Importance sampling: intrinsic dimension and computational cost
• On a generalization of the preconditioned Crank-Nicolson metropolis algorithm
• Mesh refinement and numerical sensitivity analysis for parameter calibration of partial differential equations
• Grid generation and optimization based on centroidal Voronoi tessellations
• Computability of series representations for Green's functions in a rectangle
• Model adaptivity for goal-oriented inference using adjoints
• Dimension-independent likelihood-informed MCMC
• Statistical inverse problems: discretization, model reduction and inverse crimes
• Bayesian Calibration of Computer Models
• Delayed rejection in reversible jump Metropolis-Hastings
• Adaptive Construction of Surrogates for the Bayesian Solution of Inverse Problems
• Inverse problems: A Bayesian perspective
• Data-driven model reduction for the Bayesian solution of inverse problems
• Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems
• Continuum Limits of Posteriors in Graph Bayesian Inverse Problems
• Multilevel Monte Carlo Path Simulation
• MCMC METHODS FOR DIFFUSION BRIDGES
• Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization
• Posterior consistency for Gaussian process approximations of Bayesian posterior distributions
• Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• The Bayesian formulation and well-posedness of fractional elliptic inverse problems
• Bayesian Probabilistic Numerical Methods
• The Bayesian Choice
• Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models
• On the continuum limit of a discrete inverse spectral problem on optimal finite difference grids
• MCMC methods for functions: modifying old algorithms to make them faster

This page was built for publication: Data-driven forward discretizations for Bayesian inversion