A Benchmark for the Bayesian Inversion of Coefficients in Partial Differential Equations
DOI10.1137/21m1399464arXiv2102.07263OpenAlexW3131570388MaRDI QIDQ6071826
Wolfgang Bangerth, David Aristoff
Publication date: 29 November 2023
Published in: SIAM Review (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2102.07263
inverse problemsMarkov chain Monte Carlopartial differential equationsBayesian inferencebenchmarking
Bayesian inference (62F15) Monte Carlo methods (65C05) Inverse problems in equilibrium solid mechanics (74G75) Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical analysis or methods applied to Markov chains (65C40) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)
Cites Work
- Unnamed Item
- Unnamed Item
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- Unnamed Item
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- Unnamed Item
- Ensemble samplers with affine invariance
- The Zig-Zag Process and Super-Efficient Sampling for Bayesian Analysis of Big Data
- Variance reduction using nonreversible Langevin samplers
- Optimal scaling of the random walk Metropolis on elliptically symmetric unimodal targets
- On adaptive Markov chain Monte Carlo algorithms
- On the Markov chain central limit theorem
- Exponential convergence of Langevin distributions and their discrete approximations
- Weak convergence and optimal scaling of random walk Metropolis algorithms
- Statistical and computational inverse problems.
- Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics
- Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty
- The \textsc{deal.II} finite element library: design, features, and insights
- Optimal acceptance rates for Metropolis algorithms: Moving beyond 0.234
- The \texttt{deal.II} library, version 9.4
- Randomize-Then-Optimize for Sampling and Uncertainty Quantification in Electrical Impedance Tomography
- Statistics of Parameter Estimates: A Concrete Example
- Analysis of the Hessian for inverse scattering problems: II. Inverse medium scattering of acoustic waves
- Inverse problems: A Bayesian perspective
- A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion
- Fast Algorithms for Bayesian Uncertainty Quantification in Large-Scale Linear Inverse Problems Based on Low-Rank Partial Hessian Approximations
- A Hierarchical Multilevel Markov Chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow
- Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization
- Inverse Problem Theory and Methods for Model Parameter Estimation
- Estimating Parameters in Physical Models through Bayesian Inversion: A Complete Example
- Affine Invariant Interacting Langevin Dynamics for Bayesian Inference
- hIPPYlib
- MULTIFIDELITY ESTIMATORS FOR CORONARY CIRCULATION MODELS UNDER CLINICALLY INFORMED DATA UNCERTAINTY
- Algorithm 832
- Monte Carlo sampling methods using Markov chains and their applications
- Introduction to variance estimation
- An adaptive Metropolis algorithm
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